News and updates, May 2009

May 31, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / May 31, 2009
(19·10¹⁵⁵-7)/3 = 6(3)₁₅₄1_<156> = 164235667 · 1740417311_<10> · 111425777511793_<15> · 250229323067441_<15> · C110
C110 = P49 · P62
P49 = 5281247843943756323575345174974322075624622245631_<49>
P62 = 15047039119267587349572218682986674068056537222113859655843521_<62>

Number: 63331_155 N=79467142906369303749636744937281745129764539117988920683892994469122391287838213736204396907027827898561906751 ( 110 digits) SNFS difficulty: 156 digits. Divisors found: r1=5281247843943756323575345174974322075624622245631 (pp49) r2=15047039119267587349572218682986674068056537222113859655843521 (pp62) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 36.68 hours. Scaled time: 17.31 units (timescale=0.472). Factorization parameters were as follows: name: 63331_155 n: 79467142906369303749636744937281745129764539117988920683892994469122391287838213736204396907027827898561906751 m: 10000000000000000000000000000000 deg: 5 c5: 19 c0: -7 skew: 0.82 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2200001) Primes: RFBsize:203362, AFBsize:203482, largePrimes:7899338 encountered Relations: rels:7979074, finalFF:587339 Max relations in full relation-set: 28 Initial matrix: 406909 x 587339 with sparse part having weight 60082132. Pruned matrix : 326722 x 328820 with weight 32423960. Total sieving time: 32.08 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.14 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 36.68 hours. --------- CPU info (if available) ----------

(56·10¹⁶²+61)/9 = 6(2)₁₆₁9_<163> = 13 · 17 · 333169659657218214943445880431_<30> · C131
C131 = P44 · P88
P44 = 58777162300699886134806717903601862679409189_<44>
P88 = 1437736120496800403800748865253742711720255061341109233283383300163142470662643993317611_<88>

Number: 62229_162 N=84506049300019045541148664177605664932560143115156293509081093839740279885169035460356133555067936173292757082359105087321508927479 ( 131 digits) SNFS difficulty: 163 digits. Divisors found: r1=58777162300699886134806717903601862679409189 (pp44) r2=1437736120496800403800748865253742711720255061341109233283383300163142470662643993317611 (pp88) Version: Msieve-1.40 Total time: 40.03 hours. Scaled time: 83.47 units (timescale=2.085). Factorization parameters were as follows: name: 62229_162 n: 84506049300019045541148664177605664932560143115156293509081093839740279885169035460356133555067936173292757082359105087321508927479 m: 200000000000000000000000000000000 deg: 5 c5: 175 c0: 61 skew: 0.81 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 3400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 732299 x 732547 Total sieving time: 37.56 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.01 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,163.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 40.03 hours. --------- CPU info (if available) ----------

May 31, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 31, 2009
(2·10¹⁸³+1)/3 = (6)₁₈₂7_<183> = 83 · 127 · 166561 · 45500165622286770651251939807357753869_<38> · C136
C136 = P58 · P79
P58 = 1768102116358568726804059735346898250979675156958250450963_<58>
P79 = 4719905315980089354175144342714435067318349425166521859528612903312864663830561_<79>

Number: 66667_183 N=8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243 ( 136 digits) SNFS difficulty: 185 digits. Divisors found: r1=1768102116358568726804059735346898250979675156958250450963 r2=4719905315980089354175144342714435067318349425166521859528612903312864663830561 Version: Total time: 84.74 hours. Scaled time: 202.26 units (timescale=2.387). Factorization parameters were as follows: n: 8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243 m: 10000000000000000000000000000000000000 deg: 5 c5: 1 c0: 50 skew: 2.19 type: snfs lss: 1 rlim: 6800000 alim: 6800000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 6800000/6800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [3400000, 5700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 19866084 Max relations in full relation-set: Initial matrix: Pruned matrix : 1321278 x 1321526 Total sieving time: 78.16 hours. Total relation processing time: 2.42 hours. Matrix solve time: 4.00 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,54,54,2.5,2.5,100000 total time: 84.74 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 31, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / May 30, 2009
(19·10¹⁶⁰-7)/3 = 6(3)₁₅₉1_<161> = 205559 · 166690938181_<12> · 4739551742255273_<16> · C129
C129 = P60 · P70
P60 = 192953010834035420920565005161094023397748898317016682693703_<60>
P70 = 2021133639555239274004216421272326134198633923821597116449982793956831_<70>

Number: n N=389983821050135524992495811598954671852428778933960144116705863669289820317650361573801619260957749190958138592224628970977535193 ( 129 digits) SNFS difficulty: 161 digits. Divisors found: Sat May 30 17:51:49 2009 prp60 factor: 192953010834035420920565005161094023397748898317016682693703 Sat May 30 17:51:49 2009 prp70 factor: 2021133639555239274004216421272326134198633923821597116449982793956831 Sat May 30 17:51:49 2009 elapsed time 01:13:25 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.86 hours. Scaled time: 36.20 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_3_159_1 n: 389983821050135524992495811598954671852428778933960144116705863669289820317650361573801619260957749190958138592224628970977535193 m: 100000000000000000000000000000000 deg: 5 c5: 19 c0: -7 skew: 0.82 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1700000, 2802749) Primes: RFBsize:243539, AFBsize:243539, largePrimes:9127528 encountered Relations: rels:8394159, finalFF:515146 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 677135 hash collisions in 8972024 relations Msieve: matrix is 526245 x 526493 (141.7 MB) Total sieving time: 19.72 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.3,2.3,100000 total time: 19.86 hours. --------- CPU info (if available) ----------

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 31, 2009
(19·10¹⁶⁴-7)/3 = 6(3)₁₆₃1_<165> = 521 · C163
C163 = P31 · P133
P31 = 1030395146901575232482318153521_<31>
P133 = 1179752261192165436937509834268451367995427496483506345869434991137876794024756627575257376550528314299971500543436800664584942621291_<133>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 1215611004478566858605246321177223288547664747280870121561100447856685860524632117722328854766474728087012156110044785668586052463211772232885476647472808701215611 (163 digits) Using B1=910000, B2=871204962, polynomial Dickson(3), sigma=3339709975 Step 1 took 11609ms Step 2 took 5078ms ********** Factor found in step 2: 1030395146901575232482318153521 Found probable prime factor of 31 digits: 1030395146901575232482318153521 Probable prime cofactor 1179752261192165436937509834268451367995427496483506345869434991137876794024756627575257376550528314299971500543436800664584942621291 has 133 digits

(56·10¹⁶³+61)/9 = 6(2)₁₆₂9_<164> = 3 · 547 · 36583739 · 8911817542531_<13> · C141
C141 = P41 · P100
P41 = 42597891454673060505110716648489489874029_<41>
P100 = 2730199970499644357975731595205926704022982681290973431824354119749840881511693404859673560174062129_<100>

Number: n N=116300761992895442277851487983159703948805793485901191608307239656827728210759065722462137843313433918613770797238045307858287214837429547741 ( 141 digits) SNFS difficulty: 165 digits. Divisors found: Sun May 31 01:41:53 2009 prp41 factor: 42597891454673060505110716648489489874029 Sun May 31 01:41:53 2009 prp100 factor: 2730199970499644357975731595205926704022982681290973431824354119749840881511693404859673560174062129 Sun May 31 01:41:53 2009 elapsed time 01:13:17 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 45.29 hours. Scaled time: 82.02 units (timescale=1.811). Factorization parameters were as follows: name: KA_6_2_162_9 n: 116300761992895442277851487983159703948805793485901191608307239656827728210759065722462137843313433918613770797238045307858287214837429547741 m: 400000000000000000000000000000000 deg: 5 c5: 875 c0: 976 skew: 1.02 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2000000, 4800193) Primes: RFBsize:283146, AFBsize:283248, largePrimes:16000975 encountered Relations: rels:15979828, finalFF:489412 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2015568 hash collisions in 17683124 relations Msieve: matrix is 693919 x 694167 (182.0 MB) Total sieving time: 44.58 hours. Total relation processing time: 0.71 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.4,2.4,100000 total time: 45.29 hours. --------- CPU info (if available) ----------

(56·10¹⁷⁵-11)/9 = 6(2)₁₇₄1_<176> = 47 · C175
C175 = P54 · P121
P54 = 192125247010041170809174670779335744201118561259127269_<54>
P121 = 6890698068894240356891730438060670874910112730143005165653589033348984895253689710744878953349272012244501560105878095047_<121>

Number: n N=1323877068557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643 ( 175 digits) SNFS difficulty: 177 digits. Divisors found: Sun May 31 02:43:55 2009 prp54 factor: 192125247010041170809174670779335744201118561259127269 Sun May 31 02:43:55 2009 prp121 factor: 6890698068894240356891730438060670874910112730143005165653589033348984895253689710744878953349272012244501560105878095047 Sun May 31 02:43:55 2009 elapsed time 02:23:38 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 42.54 hours. Scaled time: 113.16 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_174_1 n: 1323877068557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643 m: 200000000000000000000000000000000000 deg: 5 c5: 7 c0: -44 skew: 1.44 type: snfs lss: 1 rlim: 6400000 alim: 6400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6400000/6400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [3200000, 7810333) Primes: RFBsize:438410, AFBsize:438596, largePrimes:21022405 encountered Relations: rels:21220839, finalFF:870178 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2947888 hash collisions in 24544932 relations Msieve: matrix is 1052560 x 1052808 (277.6 MB) Total sieving time: 41.68 hours. Total relation processing time: 0.86 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,56,56,2.5,2.5,100000 total time: 42.54 hours. --------- CPU info (if available) ----------

May 31, 2009

Factorizations of 77...773 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 30, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 30, 2009
(19·10¹⁸³-7)/3 = 6(3)₁₈₂1_<184> = 13 · 2372462713_<10> · 8468765729_<10> · 69592743691_<11> · 129057352081045693_<18> · 261750565597678834213_<21> · C116
C116 = P47 · P69
P47 = 20918814650880279245782585898866372921751427107_<47>
P69 = 493058067701339029668726835528369070385382676527854413996834196777607_<69>

Number: 63331_183 N=10314190330365491502414101471530176218118047462207183441475087326449818983417302428137450255427811591623312950392949 ( 116 digits) Divisors found: r1=20918814650880279245782585898866372921751427107 r2=493058067701339029668726835528369070385382676527854413996834196777607 Version: Total time: 16.07 hours. Scaled time: 38.20 units (timescale=2.377). Factorization parameters were as follows: name: 63331_183 n: 10314190330365491502414101471530176218118047462207183441475087326449818983417302428137450255427811591623312950392949 skew: 41613.59 # norm 9.10e+15 c5: 28500 c4: 3554644580 c3: 158727902980021 c2: -3174603706020844408 c1: 21891353313746581626744 c0: -727582156817515135345185867 # alpha -6.13 Y1: 362105387977 Y0: -12933550196069224996114 # Murphy_E 5.18e-10 # M 2313767235390905646823578484813923700899760471601142099600885784234612345003558293700337149488837071365532915777600 type: gnfs rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1650000, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8690691 Max relations in full relation-set: Initial matrix: Pruned matrix : 505767 x 506015 Polynomial selection time: 1.53 hours. Total sieving time: 13.18 hours. Total relation processing time: 0.65 hours. Matrix solve time: 0.53 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000 total time: 16.07 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 30, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3 / May 30, 2009
(73·10²⁴¹-1)/9 = 8(1)_241<242> = 3 · 1553 · 3142163203150529_<16> · C223
C223 = P40 · C183
P40 = 9738217033362438978257872010279769567827_<40>
C183 = [568957009763349750886082427078689969120509026254399618771016802246504288678284189495990001284085372062009919964865734459369038780656037994148639766044103725733477699960823359523909263_<183>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1553818478 Step 1 took 16365ms Step 2 took 7596ms ********** Factor found in step 2: 9738217033362438978257872010279769567827 Found probable prime factor of 40 digits: 9738217033362438978257872010279769567827 Composite cofactor has 183 digits

May 30, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 30, 2009
(56·10¹⁶⁵+43)/9 = 6(2)₁₆₄7_<166> = 13² · 97 · C162
C162 = P54 · P109
P54 = 309696278400778819235156054633314885731808278757399009_<54>
P109 = 1225606603322051740069831254149400184276453879353393307568364058398997457686804434974933893594153486691097371_<109>

Number: n N=379565803832259026549272385909975124883927421595938645898994828415922785470763266163741976588923456488880755335949626195462833052047960850498519015568975917905339 ( 162 digits) SNFS difficulty: 166 digits. Divisors found: Sat May 30 01:58:34 2009 prp54 factor: 309696278400778819235156054633314885731808278757399009 Sat May 30 01:58:34 2009 prp109 factor: 1225606603322051740069831254149400184276453879353393307568364058398997457686804434974933893594153486691097371 Sat May 30 01:58:34 2009 elapsed time 00:54:25 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 28.06 hours. Scaled time: 74.05 units (timescale=2.639). Factorization parameters were as follows: name: KA_6_2_164_7 n: 379565803832259026549272385909975124883927421595938645898994828415922785470763266163741976588923456488880755335949626195462833052047960850498519015568975917905339 m: 1000000000000000000000000000000000 deg: 5 c5: 56 c0: 43 skew: 0.95 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2100000, 3676151) Primes: RFBsize:296314, AFBsize:296021, largePrimes:14911125 encountered Relations: rels:14135788, finalFF:539450 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1346121 hash collisions in 15874367 relations Msieve: matrix is 638603 x 638851 (171.0 MB) Total sieving time: 27.68 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000 total time: 28.06 hours. --------- CPU info (if available) ----------

(19·10¹⁶⁵-7)/3 = 6(3)₁₆₄1_<166> = 13 · 994133839 · C156
C156 = P37 · P120
P37 = 1585869221747468828672050826992090487_<37>
P120 = 309013011562915854221734443449651727484814802076522487369928457645392098079175692205271336122167806548220047231911529559_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 490054224157122952020527174892280454289193034077464070194656644395229342441867615754187379077013278470130800453699763035113001004263659492519477035103205233 (156 digits) Using B1=1216000, B2=1426326730, polynomial Dickson(6), sigma=900906112 Step 1 took 20670ms Step 2 took 7519ms ********** Factor found in step 2: 1585869221747468828672050826992090487 Found probable prime factor of 37 digits: 1585869221747468828672050826992090487 Probable prime cofactor 309013011562915854221734443449651727484814802076522487369928457645392098079175692205271336122167806548220047231911529559 has 120 digits

May 30, 2009

By Sinkiti Sibata / Msieve / May 30, 2009
(19·10¹⁴³-7)/3 = 6(3)₁₄₂1_<144> = 17 · 686946041 · 5004379399496219_<16> · C119
C119 = P49 · P70
P49 = 6064675005431407597682140703583328855985936884427_<49>
P70 = 1786911481999335182645866206956164102877404014783178509521822170053571_<70>

Number: 63331_143 N=10837037401799762698529461554216170185290795964322502951936154198933444977066459208793255063177504764001758971425638817 ( 119 digits) SNFS difficulty: 145 digits. Divisors found: r1=6064675005431407597682140703583328855985936884427 (pp49) r2=1786911481999335182645866206956164102877404014783178509521822170053571 (pp70) Version: Msieve-1.40 Total time: 11.21 hours. Scaled time: 23.45 units (timescale=2.092). Factorization parameters were as follows: name: 63331_143 n: 10837037401799762698529461554216170185290795964322502951936154198933444977066459208793255063177504764001758971425638817 m: 50000000000000000000000000000 deg: 5 c5: 152 c0: -175 skew: 1.03 type: snfs lss: 1 rlim: 1880000 alim: 1880000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1880000/1880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [940000, 2340001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 324522 x 324752 Total sieving time: 10.66 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.35 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,145.000,5,0,0,0,0,0,0,0,0,1880000,1880000,26,26,49,49,2.3,2.3,100000 total time: 11.21 hours. --------- CPU info (if available) ----------

May 29, 2009 (7th)

By Andreas Tete / GMP-ECM 6.2.3, Msieve v. 1.41 / May 29, 2009
(19·10¹⁵⁶-7)/3 = 6(3)₁₅₅1_<157> = 31² · 592451 · 43888913 · 2128275991521061911960831276960508639_<37> · C105
C105 = P32 · P73
P32 = 42922832558351566227042018293831_<32>
P73 = 2774504138001681732261294798409783710382595552789039859654944907699312713_<73>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1091934915 Step 1 took 8814ms Step 2 took 4103ms ********** Factor found in step 2: 42922832558351566227042018293831 Found probable prime factor of 32 digits: 42922832558351566227042018293831 Probable prime cofactor 2774504138001681732261294798409783710382595552789039859654944907699312713 has 73 digits

(19·10¹³⁴-7)/3 = 6(3)₁₃₃1_<135> = 3255290605655383_<16> · 1564191755329938983_<19> · C102
C102 = P44 · P58
P44 = 43633958034178706867946687302128801578332407_<44>
P58 = 2850545511538911509758997306144163361132986931822475337797_<58>

Fri May 29 01:46:11 2009 Msieve v. 1.41 Fri May 29 01:46:11 2009 random seeds: 7a0386d4 e2e4a5c6 Fri May 29 01:46:11 2009 factoring 124380583225005339635170276374626881553544663883508895938724024594535921167555826580114650203277087379 (102 digits) Fri May 29 01:46:12 2009 searching for 15-digit factors Fri May 29 01:46:13 2009 commencing number field sieve (102-digit input) Fri May 29 01:46:13 2009 R0: -41927590673415626285 Fri May 29 01:46:13 2009 R1: 31763566207 Fri May 29 01:46:13 2009 A0: 36772747658165768275752 Fri May 29 01:46:13 2009 A1: -174000147123189357426 Fri May 29 01:46:13 2009 A2: -11206915547828719 Fri May 29 01:46:13 2009 A3: 150414980036 Fri May 29 01:46:13 2009 A4: -53039818 Fri May 29 01:46:13 2009 A5: 960 Fri May 29 01:46:13 2009 skew 18483.41, size 1.224183e-009, alpha -4.909780, combined = 2.906612e-009 Fri May 29 01:46:14 2009 Fri May 29 01:46:14 2009 commencing relation filtering Fri May 29 01:46:14 2009 commencing duplicate removal, pass 1 Fri May 29 01:47:30 2009 found 392433 hash collisions in 4779022 relations Fri May 29 01:47:43 2009 added 30939 free relations Fri May 29 01:47:43 2009 commencing duplicate removal, pass 2 Fri May 29 01:48:03 2009 found 376855 duplicates and 4433105 unique relations Fri May 29 01:48:03 2009 memory use: 40.3 MB Fri May 29 01:48:03 2009 reading rational ideals above 2031616 Fri May 29 01:48:03 2009 reading algebraic ideals above 2031616 Fri May 29 01:48:03 2009 commencing singleton removal, pass 1 Fri May 29 01:48:49 2009 relations with 0 large ideals: 80551 Fri May 29 01:48:49 2009 relations with 1 large ideals: 590268 Fri May 29 01:48:49 2009 relations with 2 large ideals: 1517218 Fri May 29 01:48:49 2009 relations with 3 large ideals: 1590960 Fri May 29 01:48:49 2009 relations with 4 large ideals: 586066 Fri May 29 01:48:49 2009 relations with 5 large ideals: 38047 Fri May 29 01:48:49 2009 relations with 6 large ideals: 29992 Fri May 29 01:48:49 2009 relations with 7+ large ideals: 3 Fri May 29 01:48:49 2009 4433105 relations and about 4216507 large ideals Fri May 29 01:48:49 2009 commencing singleton removal, pass 2 Fri May 29 01:49:36 2009 found 1920217 singletons Fri May 29 01:49:36 2009 current dataset: 2512888 relations and about 1933737 large ideals Fri May 29 01:49:36 2009 commencing singleton removal, pass 3 Fri May 29 01:50:12 2009 found 390516 singletons Fri May 29 01:50:12 2009 current dataset: 2122372 relations and about 1520986 large ideals Fri May 29 01:50:12 2009 commencing singleton removal, final pass Fri May 29 01:50:53 2009 memory use: 34.5 MB Fri May 29 01:50:53 2009 commencing in-memory singleton removal Fri May 29 01:50:53 2009 begin with 2122372 relations and 1562809 unique ideals Fri May 29 01:50:55 2009 reduce to 1898971 relations and 1334953 ideals in 10 passes Fri May 29 01:50:55 2009 max relations containing the same ideal: 67 Fri May 29 01:50:55 2009 reading rational ideals above 100000 Fri May 29 01:50:55 2009 reading algebraic ideals above 100000 Fri May 29 01:50:55 2009 commencing singleton removal, final pass Fri May 29 01:51:43 2009 keeping 1538216 ideals with weight <= 25, new excess is 126334 Fri May 29 01:51:46 2009 memory use: 47.3 MB Fri May 29 01:51:46 2009 commencing in-memory singleton removal Fri May 29 01:51:46 2009 begin with 1903679 relations and 1538216 unique ideals Fri May 29 01:51:48 2009 reduce to 1897608 relations and 1509334 ideals in 8 passes Fri May 29 01:51:48 2009 max relations containing the same ideal: 25 Fri May 29 01:51:49 2009 removing 522496 relations and 401633 ideals in 120863 cliques Fri May 29 01:51:49 2009 commencing in-memory singleton removal Fri May 29 01:51:49 2009 begin with 1375112 relations and 1509334 unique ideals Fri May 29 01:51:51 2009 reduce to 1297128 relations and 1024266 ideals in 8 passes Fri May 29 01:51:51 2009 max relations containing the same ideal: 25 Fri May 29 01:51:51 2009 removing 397287 relations and 276424 ideals in 120863 cliques Fri May 29 01:51:51 2009 commencing in-memory singleton removal Fri May 29 01:51:52 2009 begin with 899841 relations and 1024266 unique ideals Fri May 29 01:51:52 2009 reduce to 824971 relations and 666110 ideals in 8 passes Fri May 29 01:51:52 2009 max relations containing the same ideal: 21 Fri May 29 01:51:53 2009 removing 67837 relations and 55524 ideals in 12313 cliques Fri May 29 01:51:53 2009 commencing in-memory singleton removal Fri May 29 01:51:53 2009 begin with 757134 relations and 666110 unique ideals Fri May 29 01:51:53 2009 reduce to 753786 relations and 607197 ideals in 6 passes Fri May 29 01:51:53 2009 max relations containing the same ideal: 21 Fri May 29 01:51:53 2009 relations with 0 large ideals: 11066 Fri May 29 01:51:53 2009 relations with 1 large ideals: 73648 Fri May 29 01:51:53 2009 relations with 2 large ideals: 190050 Fri May 29 01:51:53 2009 relations with 3 large ideals: 242532 Fri May 29 01:51:53 2009 relations with 4 large ideals: 162951 Fri May 29 01:51:53 2009 relations with 5 large ideals: 59782 Fri May 29 01:51:53 2009 relations with 6 large ideals: 12446 Fri May 29 01:51:53 2009 relations with 7+ large ideals: 1311 Fri May 29 01:51:53 2009 commencing 2-way merge Fri May 29 01:51:53 2009 reduce to 487336 relation sets and 340747 unique ideals Fri May 29 01:51:53 2009 commencing full merge Fri May 29 01:51:59 2009 memory use: 25.5 MB Fri May 29 01:51:59 2009 found 230072 cycles, need 210947 Fri May 29 01:51:59 2009 weight of 210947 cycles is about 14775600 (70.04/cycle) Fri May 29 01:51:59 2009 distribution of cycle lengths: Fri May 29 01:51:59 2009 1 relations: 18697 Fri May 29 01:51:59 2009 2 relations: 18637 Fri May 29 01:51:59 2009 3 relations: 19991 Fri May 29 01:51:59 2009 4 relations: 19889 Fri May 29 01:51:59 2009 5 relations: 19620 Fri May 29 01:51:59 2009 6 relations: 18220 Fri May 29 01:51:59 2009 7 relations: 16848 Fri May 29 01:51:59 2009 8 relations: 15336 Fri May 29 01:51:59 2009 9 relations: 13673 Fri May 29 01:51:59 2009 10+ relations: 50036 Fri May 29 01:51:59 2009 heaviest cycle: 18 relations Fri May 29 01:51:59 2009 commencing cycle optimization Fri May 29 01:51:59 2009 start with 1374954 relations Fri May 29 01:52:03 2009 pruned 52307 relations Fri May 29 01:52:03 2009 memory use: 33.9 MB Fri May 29 01:52:03 2009 distribution of cycle lengths: Fri May 29 01:52:03 2009 1 relations: 18697 Fri May 29 01:52:03 2009 2 relations: 19181 Fri May 29 01:52:03 2009 3 relations: 21002 Fri May 29 01:52:03 2009 4 relations: 20738 Fri May 29 01:52:03 2009 5 relations: 20663 Fri May 29 01:52:03 2009 6 relations: 19137 Fri May 29 01:52:03 2009 7 relations: 17544 Fri May 29 01:52:03 2009 8 relations: 15854 Fri May 29 01:52:03 2009 9 relations: 13910 Fri May 29 01:52:03 2009 10+ relations: 44221 Fri May 29 01:52:03 2009 heaviest cycle: 18 relations Fri May 29 01:52:03 2009 RelProcTime: 249 Fri May 29 01:52:03 2009 Fri May 29 01:52:03 2009 commencing linear algebra Fri May 29 01:52:03 2009 read 210947 cycles Fri May 29 01:52:04 2009 cycles contain 673540 unique relations Fri May 29 01:52:25 2009 read 673540 relations Fri May 29 01:52:26 2009 using 20 quadratic characters above 67108290 Fri May 29 01:52:30 2009 building initial matrix Fri May 29 01:52:40 2009 memory use: 75.2 MB Fri May 29 01:52:40 2009 read 210947 cycles Fri May 29 01:52:40 2009 matrix is 210749 x 210947 (58.5 MB) with weight 19798822 (93.86/col) Fri May 29 01:52:40 2009 sparse part has weight 13848264 (65.65/col) Fri May 29 01:52:43 2009 filtering completed in 2 passes Fri May 29 01:52:43 2009 matrix is 210230 x 210428 (58.4 MB) with weight 19766738 (93.94/col) Fri May 29 01:52:43 2009 sparse part has weight 13831777 (65.73/col) Fri May 29 01:52:44 2009 read 210428 cycles Fri May 29 01:52:45 2009 matrix is 210230 x 210428 (58.4 MB) with weight 19766738 (93.94/col) Fri May 29 01:52:45 2009 sparse part has weight 13831777 (65.73/col) Fri May 29 01:52:45 2009 saving the first 48 matrix rows for later Fri May 29 01:52:45 2009 matrix is 210182 x 210428 (55.9 MB) with weight 15466001 (73.50/col) Fri May 29 01:52:45 2009 sparse part has weight 13378511 (63.58/col) Fri May 29 01:52:45 2009 matrix includes 64 packed rows Fri May 29 01:52:45 2009 using block size 65536 for processor cache size 3072 kB Fri May 29 01:52:47 2009 commencing Lanczos iteration Fri May 29 01:52:47 2009 memory use: 53.9 MB Fri May 29 01:58:49 2009 lanczos halted after 3325 iterations (dim = 210182) Fri May 29 01:58:50 2009 recovered 32 nontrivial dependencies Fri May 29 01:58:50 2009 BLanczosTime: 407 Fri May 29 01:58:50 2009 Fri May 29 01:58:50 2009 commencing square root phase Fri May 29 01:58:50 2009 reading relations for dependency 1 Fri May 29 01:58:50 2009 read 105203 cycles Fri May 29 01:58:50 2009 cycles contain 423488 unique relations Fri May 29 01:58:56 2009 read 423488 relations Fri May 29 01:58:58 2009 multiplying 336942 relations Fri May 29 01:59:40 2009 multiply complete, coefficients have about 12.53 million bits Fri May 29 01:59:40 2009 initial square root is modulo 15873877 Fri May 29 02:00:39 2009 sqrtTime: 109 Fri May 29 02:00:39 2009 prp44 factor: 43633958034178706867946687302128801578332407 Fri May 29 02:00:39 2009 prp58 factor: 2850545511538911509758997306144163361132986931822475337797 Fri May 29 02:00:39 2009 elapsed time 00:14:28 total time ~ 6 hours

May 29, 2009 (6th)

By Sinkiti Sibata / Msieve, GGNFS / May 29, 2009
(19·10¹²⁴-7)/3 = 6(3)₁₂₃1_<125> = 51753967471_<11> · C115
C115 = P42 · P73
P42 = 334097884150240049775907767539422981255259_<42>
P73 = 3662814902318079871210119531219746089941789043300847960174770283548307879_<73>

Number: 63331_124 N=1223738708898438673158498521971862166326037441608479951609106141089519589487113261963145490831491374404224819885661 ( 115 digits) SNFS difficulty: 126 digits. Divisors found: r1=334097884150240049775907767539422981255259 (pp42) r2=3662814902318079871210119531219746089941789043300847960174770283548307879 (pp73) Version: Msieve-1.40 Total time: 2.21 hours. Scaled time: 4.28 units (timescale=1.939). Factorization parameters were as follows: name: 63331_124 n: 1223738708898438673158498521971862166326037441608479951609106141089519589487113261963145490831491374404224819885661 m: 10000000000000000000000000 deg: 5 c5: 19 c0: -70 skew: 1.30 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 745001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 129222 x 129450 Total sieving time: 2.10 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 2.21 hours. --------- CPU info (if available) ----------

(19·10¹⁴¹-7)/3 = 6(3)₁₄₀1_<142> = 13 · 31 · 121823874281_<12> · 1054160869936423_<16> · C114
C114 = P47 · P67
P47 = 32436080587219098362111053786648781396373526097_<47>
P67 = 3772763927878618428978561857091666143636833194970166981744931256207_<67>

Number: 63331_141 N=122373674801224129713801839644924727291412501484302854678154146032811270477033116336772352870157465546636307734079 ( 114 digits) SNFS difficulty: 143 digits. Divisors found: r1=32436080587219098362111053786648781396373526097 (pp47) r2=3772763927878618428978561857091666143636833194970166981744931256207 (pp67) Version: Msieve-1.40 Total time: 6.64 hours. Scaled time: 13.90 units (timescale=2.092). Factorization parameters were as follows: name: 63331_141 n: 122373674801224129713801839644924727291412501484302854678154146032811270477033116336772352870157465546636307734079 m: 20000000000000000000000000000 deg: 5 c5: 95 c0: -112 skew: 1.03 type: snfs lss: 1 rlim: 1720000 alim: 1720000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1720000/1720000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [860000, 1660001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 224336 x 224584 Total sieving time: 6.38 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.17 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,143.000,5,0,0,0,0,0,0,0,0,1720000,1720000,26,26,48,48,2.3,2.3,100000 total time: 6.64 hours. --------- CPU info (if available) ----------

(19·10¹⁴⁶-7)/3 = 6(3)₁₄₅1_<147> = C147
C147 = P47 · P100
P47 = 77171271388291014287393251838556984620187665647_<47>
P100 = 8206853689719400760471490320870429786719891558871093340652371961062720153762369224195693688837201373_<100>

Number: 63331_146 N=633333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 147 digits) SNFS difficulty: 148 digits. Divisors found: r1=77171271388291014287393251838556984620187665647 (pp47) r2=8206853689719400760471490320870429786719891558871093340652371961062720153762369224195693688837201373 (pp100) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 17.57 hours. Scaled time: 7.56 units (timescale=0.430). Factorization parameters were as follows: name: 63331_146 n: 633333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 200000000000000000000000000000 deg: 5 c5: 95 c0: -112 skew: 1.03 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2250001) Primes: RFBsize:155805, AFBsize:155117, largePrimes:4100927 encountered Relations: rels:4170193, finalFF:377449 Max relations in full relation-set: 28 Initial matrix: 310989 x 377449 with sparse part having weight 32749524. Pruned matrix : 283655 x 285273 with weight 21193066. Total sieving time: 14.85 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.41 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 17.57 hours. --------- CPU info (if available) ----------

May 29, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 29, 2009
(56·10¹⁸⁶+61)/9 = 6(2)₁₈₅9_<187> = 13 · 84061 · 1822669 · 443936293 · 203796075559_<12> · 439766607999421_<15> · 386006825772686319809_<21> · C120
C120 = P51 · P69
P51 = 250673953247691140295576769478106793315213729261069_<51>
P69 = 811440899328768309046496122133133937558453179540215891652660246798611_<69>

Number: 62229_186 N=203407098061604120287021780643889425783415179229077710477149813168419812392713855634930663385611053845841843301885575159 ( 120 digits) Divisors found: r1=250673953247691140295576769478106793315213729261069 r2=811440899328768309046496122133133937558453179540215891652660246798611 Version: Total time: 28.47 hours. Scaled time: 68.07 units (timescale=2.391). Factorization parameters were as follows: name: 62229_186 n: 203407098061604120287021780643889425783415179229077710477149813168419812392713855634930663385611053845841843301885575159 skew: 50983.71 # norm 1.83e+16 c5: 29940 c4: 8871972664 c3: 133501584474317 c2: -18333168317553189533 c1: 397303272440526758105387 c0: -2454440886303536665977967575 # alpha -5.21 Y1: 9371863989197 Y0: -92559341351746858589674 # Murphy_E 2.93e-10 # M 22682978338461827122610808507135925082005800740391586673361601427470149998450196025368237394910875482716387709003550593 type: gnfs rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [2400000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10199974 Max relations in full relation-set: Initial matrix: Pruned matrix : 733110 x 733358 Polynomial selection time: 2.61 hours. Total sieving time: 23.59 hours. Total relation processing time: 0.98 hours. Matrix solve time: 1.13 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4800000,4800000,27,27,53,53,2.4,2.4,100000 total time: 28.47 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 29, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / May 29, 2009
(49·10¹⁶⁸-31)/9 = 5(4)₁₆₇1_<169> = 15301755193_<11> · 13943954834566879_<17> · 2810066056947827497_<19> · C124
C124 = P46 · P79
P46 = 2738071186438710195874120880465381105300462749_<46>
P79 = 3316386124839130067412276341415290040498997690391963192414696202873340504719251_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=408812994 Step 1 took 34039ms Step 2 took 13682ms ********** Factor found in step 2: 2738071186438710195874120880465381105300462749 Found probable prime factor of 46 digits: 2738071186438710195874120880465381105300462749 Probable prime cofactor 3316386124839130067412276341415290040498997690391963192414696202873340504719251 has 79 digits

May 29, 2009 (3rd)

By matsui / Msieve / May 29, 2009
9·10¹⁷¹-1 = 8(9)_171<172> = 136963579157_<12> · 429373702687757_<15> · C147
C147 = P47 · P100
P47 = 42679129855580064934964485511968838445123658843_<47>
P100 = 3585802901069120875169780945172816193378262142753545298800676974244410697305766876766285241909080157_<100>

N=153038947651244726688666449207685636156794373899467047177951914194053059387772278586968400747355401308035645995849761200170389692110687828408878351 ( 147 digits) SNFS difficulty: 173 digits. Divisors found: r1=42679129855580064934964485511968838445123658843 (pp47) r2=3585802901069120875169780945172816193378262142753545298800676974244410697305766876766285241909080157 (pp100) Version: Msieve v. 1.41 Total time: 78.73 hours. Scaled time: 174.07 units (timescale=2.211). Factorization parameters were as follows: n: 153038947651244726688666449207685636156794373899467047177951914194053059387772278586968400747355401308035645995849761200170389692110687828408878351 m: 30000000000000000000000000000000000 deg: 5 c5: 10 c0: -27 skew: 1.22 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 300000 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2700000, 6000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 945937 x 946185 Total sieving time: 76.03 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.28 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: snfs,173.000,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000 total time: 78.73 hours.

9·10²⁴⁹-1 = 8(9)_249<250> = 1239961 · 17567289930891241_<17> · 2211131180516999698877_<22> · 132852679081112049264025722783994751_<36> · 173971508153106043979381596158458837_<36> · C136
C136 = P59 · P78
P59 = 12401770836281816440614430558156356059434053950562553627081_<59>
P78 = 651903118776272291480393446015384353260696868728533727242356292283467348358521_<78>

N=8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201 ( 136 digits) Divisors found: r1=12401770836281816440614430558156356059434053950562553627081 (pp59) r2=651903118776272291480393446015384353260696868728533727242356292283467348358521 (pp78) Version: Msieve v. 1.41 Total time: 226.30 hours. Scaled time: 501.03 units (timescale=2.214). Factorization parameters were as follows: n: 8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201 m: c5: 720360 c4: -1815557350383 c3: -23809703162461182 c2: 28998780185371742771312 c1: 325033929753928457456535728 c0: -26134567168271472059124246564480 Y1: 1303012087128367 Y0: -102335477824812549114012973 skew: 136467.92 type: gnfs rlim: 9800000 alim: 9800000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 9800000/9800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved algebraic special-q in [4900000, 9600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1702773 x 1703021 Total sieving time: 220.58 hours. Total relation processing time: 0.26 hours. Matrix solve time: 5.01 hours. Time per square root: 0.44 hours. Prototype def-par.txt line would be: gnfs,135,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,9800000,9800000,28,28,55,55,2.5,2.5,100000 total time: 226.30 hours.

May 29, 2009 (2nd)

By Robert Backstrom / GGNFS / May 29, 2009
(19·10¹³³-7)/3 = 6(3)₁₃₂1_<134> = 825593 · C128
C128 = P63 · P66
P63 = 276917410651474473427328257365491996984371079112664023186244621_<63>
P66 = 277023162052734203341720293109298019669320818393106271797699685527_<66>

Number: n N=76712536726126957633280966933262919299622614694326784908948275158986732364898119694974803969187400248467868953992261723795300267 ( 128 digits) SNFS difficulty: 135 digits. Divisors found: r1=276917410651474473427328257365491996984371079112664023186244621 (pp63) r2=277023162052734203341720293109298019669320818393106271797699685527 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.98 hours. Scaled time: 7.28 units (timescale=1.829). Factorization parameters were as follows: name: KA_6_3_132_1 n: 76712536726126957633280966933262919299622614694326784908948275158986732364898119694974803969187400248467868953992261723795300267 m: 500000000000000000000000000 deg: 5 c5: 152 c0: -175 skew: 1.03 type: snfs lss: 1 rlim: 1280000 alim: 1280000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 1280000/1280000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [640000, 1340001) Primes: RFBsize:98610, AFBsize:98660, largePrimes:5291294 encountered Relations: rels:4679338, finalFF:255913 Max relations in full relation-set: 48 Initial matrix: 197337 x 255913 with sparse part having weight 27792419. Pruned matrix : 182759 x 183809 with weight 14545692. Total sieving time: 3.54 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.25 hours. Total square root time: 0.12 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1280000,1280000,28,28,56,56,2.3,2.3,75000 total time: 3.98 hours. --------- CPU info (if available) ----------

May 29, 2009

By Serge Batalov / GMP-ECM 6.2.3 / May 29, 2009
(19·10¹⁷⁶-7)/3 = 6(3)₁₇₅1_<177> = 3499 · 17881 · 20441 · 79357 · C160
C160 = P37 · P124
P37 = 3163772207346213559008453427361628107_<37>
P124 = 1972440967760531199381211837488119430417008472869108795319192731868746765494186479794291931702613136217821449591778270468311_<124>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2707555263 Step 1 took 11868ms Step 2 took 11053ms ********** Factor found in step 2: 3163772207346213559008453427361628107 Found probable prime factor of 37 digits: 3163772207346213559008453427361628107 Probable prime cofactor has 124 digits

May 28, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / May 28, 2009
(56·10¹⁶¹+61)/9 = 6(2)₁₆₀9_<162> = 37 · C161
C161 = P68 · P94
P68 = 13048995793706679358357176909020251049647095744876594597880337395921_<68>
P94 = 1288744136535571334391285850180075374337949769163721716371914833115868776095281688468705962977_<94>

Number: 62229_161 N=16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817 ( 161 digits) SNFS difficulty: 163 digits. Divisors found: r1=13048995793706679358357176909020251049647095744876594597880337395921 (pp68) r2=1288744136535571334391285850180075374337949769163721716371914833115868776095281688468705962977 (pp94) Version: Msieve-1.40 Total time: 45.84 hours. Scaled time: 95.57 units (timescale=2.085). Factorization parameters were as follows: name: 62229_161 n: 16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817 m: 200000000000000000000000000000000 deg: 5 c5: 35 c0: 122 skew: 1.28 type: snfs lss: 1 rlim: 3700000 alim: 3700000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3700000/3700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1850000, 3650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 660498 x 660746 Total sieving time: 43.92 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.59 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,163.000,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000 total time: 45.84 hours. --------- CPU info (if available) ----------

(19·10¹⁵⁸-7)/3 = 6(3)₁₅₇1_<159> = 12748061 · 244988506811_<12> · 3945162826217_<13> · 183252155785867837_<18> · 555494520034835752099_<21> · C90
C90 = P28 · P62
P28 = 5576034521395138710161741431_<28>
P62 = 90557254071447654817328327205076133848394476380414258694325861_<62>

Thu May 28 17:28:03 2009 Msieve v. 1.41 Thu May 28 17:28:03 2009 random seeds: f671fa40 5246c742 Thu May 28 17:28:03 2009 factoring 504950374865142600275495635504678889561884596942536208080854606867393688609203766338447091 (90 digits) Thu May 28 17:28:04 2009 searching for 15-digit factors Thu May 28 17:28:06 2009 commencing quadratic sieve (90-digit input) Thu May 28 17:28:06 2009 using multiplier of 3 Thu May 28 17:28:06 2009 using 32kb Intel Core sieve core Thu May 28 17:28:06 2009 sieve interval: 36 blocks of size 32768 Thu May 28 17:28:06 2009 processing polynomials in batches of 6 Thu May 28 17:28:06 2009 using a sieve bound of 1584931 (59873 primes) Thu May 28 17:28:06 2009 using large prime bound of 126794480 (26 bits) Thu May 28 17:28:06 2009 using double large prime bound of 385106280791040 (42-49 bits) Thu May 28 17:28:06 2009 using trial factoring cutoff of 49 bits Thu May 28 17:28:06 2009 polynomial 'A' values have 12 factors Thu May 28 18:45:55 2009 60302 relations (15971 full + 44331 combined from 641278 partial), need 59969 Thu May 28 18:45:56 2009 begin with 657249 relations Thu May 28 18:45:56 2009 reduce to 147005 relations in 11 passes Thu May 28 18:45:56 2009 attempting to read 147005 relations Thu May 28 18:45:58 2009 recovered 147005 relations Thu May 28 18:45:58 2009 recovered 126900 polynomials Thu May 28 18:45:58 2009 attempting to build 60302 cycles Thu May 28 18:45:58 2009 found 60302 cycles in 6 passes Thu May 28 18:45:58 2009 distribution of cycle lengths: Thu May 28 18:45:58 2009 length 1 : 15971 Thu May 28 18:45:58 2009 length 2 : 11649 Thu May 28 18:45:58 2009 length 3 : 10712 Thu May 28 18:45:58 2009 length 4 : 8110 Thu May 28 18:45:58 2009 length 5 : 5770 Thu May 28 18:45:58 2009 length 6 : 3416 Thu May 28 18:45:58 2009 length 7 : 2145 Thu May 28 18:45:58 2009 length 9+: 2529 Thu May 28 18:45:58 2009 largest cycle: 20 relations Thu May 28 18:45:59 2009 matrix is 59873 x 60302 (14.8 MB) with weight 3649006 (60.51/col) Thu May 28 18:45:59 2009 sparse part has weight 3649006 (60.51/col) Thu May 28 18:46:00 2009 filtering completed in 3 passes Thu May 28 18:46:00 2009 matrix is 55912 x 55976 (13.8 MB) with weight 3395133 (60.65/col) Thu May 28 18:46:00 2009 sparse part has weight 3395133 (60.65/col) Thu May 28 18:46:00 2009 saving the first 48 matrix rows for later Thu May 28 18:46:00 2009 matrix is 55864 x 55976 (9.1 MB) with weight 2710920 (48.43/col) Thu May 28 18:46:00 2009 sparse part has weight 2037212 (36.39/col) Thu May 28 18:46:00 2009 matrix includes 64 packed rows Thu May 28 18:46:00 2009 using block size 22390 for processor cache size 1024 kB Thu May 28 18:46:00 2009 commencing Lanczos iteration Thu May 28 18:46:00 2009 memory use: 8.6 MB Thu May 28 18:46:19 2009 lanczos halted after 884 iterations (dim = 55861) Thu May 28 18:46:19 2009 recovered 16 nontrivial dependencies Thu May 28 18:46:20 2009 prp28 factor: 5576034521395138710161741431 Thu May 28 18:46:20 2009 prp62 factor: 90557254071447654817328327205076133848394476380414258694325861 Thu May 28 18:46:20 2009 elapsed time 01:18:17

(19·10¹⁰⁷-7)/3 = 6(3)₁₀₆1_<108> = 5063453251223820049_<19> · C90
C90 = P41 · P49
P41 = 27699069066082335842545359049149492434657_<41>
P49 = 4515650990127709404839488960748228699356811540867_<49>

Thu May 28 17:24:09 2009 Msieve v. 1.39 Thu May 28 17:24:09 2009 random seeds: 7f5bdf80 2937e844 Thu May 28 17:24:09 2009 factoring 125079328653870506893939709139555539629227686655558726451828266925280542002683923482627619 (90 digits) Thu May 28 17:24:10 2009 searching for 15-digit factors Thu May 28 17:24:12 2009 commencing quadratic sieve (90-digit input) Thu May 28 17:24:13 2009 using multiplier of 19 Thu May 28 17:24:13 2009 using 64kb Pentium 4 sieve core Thu May 28 17:24:13 2009 sieve interval: 17 blocks of size 65536 Thu May 28 17:24:13 2009 processing polynomials in batches of 6 Thu May 28 17:24:13 2009 using a sieve bound of 1565693 (59275 primes) Thu May 28 17:24:13 2009 using large prime bound of 125255440 (26 bits) Thu May 28 17:24:13 2009 using double large prime bound of 376733166741360 (42-49 bits) Thu May 28 17:24:13 2009 using trial factoring cutoff of 49 bits Thu May 28 17:24:13 2009 polynomial 'A' values have 12 factors Thu May 28 20:01:23 2009 59872 relations (15512 full + 44360 combined from 636070 partial), need 59371 Thu May 28 20:01:23 2009 begin with 651582 relations Thu May 28 20:01:24 2009 reduce to 147624 relations in 9 passes Thu May 28 20:01:24 2009 attempting to read 147624 relations Thu May 28 20:01:26 2009 recovered 147624 relations Thu May 28 20:01:26 2009 recovered 129772 polynomials Thu May 28 20:01:26 2009 attempting to build 59872 cycles Thu May 28 20:01:26 2009 found 59872 cycles in 5 passes Thu May 28 20:01:26 2009 distribution of cycle lengths: Thu May 28 20:01:26 2009 length 1 : 15512 Thu May 28 20:01:26 2009 length 2 : 11355 Thu May 28 20:01:26 2009 length 3 : 10603 Thu May 28 20:01:26 2009 length 4 : 8064 Thu May 28 20:01:26 2009 length 5 : 5649 Thu May 28 20:01:26 2009 length 6 : 3749 Thu May 28 20:01:26 2009 length 7 : 2267 Thu May 28 20:01:26 2009 length 9+: 2673 Thu May 28 20:01:26 2009 largest cycle: 17 relations Thu May 28 20:01:27 2009 matrix is 59275 x 59872 (14.6 MB) with weight 3590614 (59.97/col) Thu May 28 20:01:27 2009 sparse part has weight 3590614 (59.97/col) Thu May 28 20:01:28 2009 filtering completed in 3 passes Thu May 28 20:01:28 2009 matrix is 55768 x 55831 (13.6 MB) with weight 3342235 (59.86/col) Thu May 28 20:01:28 2009 sparse part has weight 3342235 (59.86/col) Thu May 28 20:01:28 2009 saving the first 48 matrix rows for later Thu May 28 20:01:28 2009 matrix is 55720 x 55831 (8.6 MB) with weight 2634322 (47.18/col) Thu May 28 20:01:28 2009 sparse part has weight 1910383 (34.22/col) Thu May 28 20:01:28 2009 matrix includes 64 packed rows Thu May 28 20:01:28 2009 using block size 21845 for processor cache size 512 kB Thu May 28 20:01:29 2009 commencing Lanczos iteration Thu May 28 20:01:29 2009 memory use: 8.4 MB Thu May 28 20:01:58 2009 lanczos halted after 883 iterations (dim = 55718) Thu May 28 20:01:59 2009 recovered 16 nontrivial dependencies Thu May 28 20:01:59 2009 prp41 factor: 27699069066082335842545359049149492434657 Thu May 28 20:01:59 2009 prp49 factor: 4515650990127709404839488960748228699356811540867 Thu May 28 20:01:59 2009 elapsed time 02:37:50

(19·10¹¹³-7)/3 = 6(3)₁₁₂1_<114> = 8559317557642312663_<19> · C95
C95 = P36 · P60
P36 = 364273749615784181999930257926974317_<36>
P60 = 203125913174411006540302087331278541353649937784127457423961_<60>

Thu May 28 18:56:30 2009 Msieve v. 1.41 Thu May 28 18:56:31 2009 random seeds: 06c371f0 c3b8ef42 Thu May 28 18:56:31 2009 factoring 73993438036172912506392899516636791785351321648353676280690625853787679718172923974499827409637 (95 digits) Thu May 28 18:56:31 2009 searching for 15-digit factors Thu May 28 18:56:33 2009 commencing quadratic sieve (95-digit input) Thu May 28 18:56:33 2009 using multiplier of 7 Thu May 28 18:56:33 2009 using 32kb Intel Core sieve core Thu May 28 18:56:33 2009 sieve interval: 36 blocks of size 32768 Thu May 28 18:56:33 2009 processing polynomials in batches of 6 Thu May 28 18:56:33 2009 using a sieve bound of 2189221 (81176 primes) Thu May 28 18:56:33 2009 using large prime bound of 328383150 (28 bits) Thu May 28 18:56:33 2009 using double large prime bound of 2135430964341600 (43-51 bits) Thu May 28 18:56:33 2009 using trial factoring cutoff of 51 bits Thu May 28 18:56:33 2009 polynomial 'A' values have 12 factors Thu May 28 22:25:59 2009 81333 relations (20466 full + 60867 combined from 1206902 partial), need 81272 Thu May 28 22:26:01 2009 begin with 1227368 relations Thu May 28 22:26:02 2009 reduce to 209918 relations in 11 passes Thu May 28 22:26:02 2009 attempting to read 209918 relations Thu May 28 22:26:05 2009 recovered 209918 relations Thu May 28 22:26:05 2009 recovered 192815 polynomials Thu May 28 22:26:05 2009 attempting to build 81333 cycles Thu May 28 22:26:06 2009 found 81333 cycles in 6 passes Thu May 28 22:26:06 2009 distribution of cycle lengths: Thu May 28 22:26:06 2009 length 1 : 20466 Thu May 28 22:26:06 2009 length 2 : 14388 Thu May 28 22:26:06 2009 length 3 : 13712 Thu May 28 22:26:06 2009 length 4 : 11051 Thu May 28 22:26:06 2009 length 5 : 8178 Thu May 28 22:26:06 2009 length 6 : 5546 Thu May 28 22:26:06 2009 length 7 : 3416 Thu May 28 22:26:06 2009 length 9+: 4576 Thu May 28 22:26:06 2009 largest cycle: 19 relations Thu May 28 22:26:06 2009 matrix is 81176 x 81333 (22.4 MB) with weight 5559794 (68.36/col) Thu May 28 22:26:06 2009 sparse part has weight 5559794 (68.36/col) Thu May 28 22:26:07 2009 filtering completed in 4 passes Thu May 28 22:26:07 2009 matrix is 77022 x 77086 (21.4 MB) with weight 5309405 (68.88/col) Thu May 28 22:26:07 2009 sparse part has weight 5309405 (68.88/col) Thu May 28 22:26:07 2009 saving the first 48 matrix rows for later Thu May 28 22:26:08 2009 matrix is 76974 x 77086 (15.4 MB) with weight 4400031 (57.08/col) Thu May 28 22:26:08 2009 sparse part has weight 3582618 (46.48/col) Thu May 28 22:26:08 2009 matrix includes 64 packed rows Thu May 28 22:26:08 2009 using block size 30834 for processor cache size 1024 kB Thu May 28 22:26:09 2009 commencing Lanczos iteration Thu May 28 22:26:09 2009 memory use: 13.7 MB Thu May 28 22:26:53 2009 lanczos halted after 1219 iterations (dim = 76972) Thu May 28 22:26:53 2009 recovered 17 nontrivial dependencies Thu May 28 22:26:55 2009 prp36 factor: 364273749615784181999930257926974317 Thu May 28 22:26:55 2009 prp60 factor: 203125913174411006540302087331278541353649937784127457423961 Thu May 28 22:26:55 2009 elapsed time 03:30:24

(19·10¹¹⁹-7)/3 = 6(3)₁₁₈1_<120> = 2213 · 5749978691_<10> · C107
C107 = P52 · P55
P52 = 7142565667777428842404199142177757024839466055246647_<52>
P55 = 6968358010744748481904859785034423037844326555299193931_<55>

Number: 63331_119 N=49771954688327260109155339961234952205510402352405246631726248886182137604135641201297364629821392490499357 ( 107 digits) SNFS difficulty: 121 digits. Divisors found: r1=7142565667777428842404199142177757024839466055246647 (pp52) r2=6968358010744748481904859785034423037844326555299193931 (pp55) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.02 hours. Scaled time: 1.43 units (timescale=0.473). Factorization parameters were as follows: name: 63331_119 n: 49771954688327260109155339961234952205510402352405246631726248886182137604135641201297364629821392490499357 m: 1000000000000000000000000 deg: 5 c5: 19 c0: -70 skew: 1.30 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 670001) Primes: RFBsize:59531, AFBsize:59488, largePrimes:1388071 encountered Relations: rels:1389636, finalFF:174888 Max relations in full relation-set: 28 Initial matrix: 119084 x 174888 with sparse part having weight 8851867. Pruned matrix : 98634 x 99293 with weight 3731877. Total sieving time: 2.86 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 3.02 hours. --------- CPU info (if available) ----------

May 28, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / May 28, 2009
(32·10¹⁶⁹+31)/9 = 3(5)₁₆₈9_<170> = 3 · 13 · 17 · 3229 · 319549142894958130531092345559_<30> · C134
C134 = P47 · P88
P47 = 36503865295478130758755327213624903058483920561_<47>
P88 = 1423801300523414982742214232334802997389942436426180599813692010039144526423143680899283_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1504946988 Step 1 took 38186ms Step 2 took 14458ms ********** Factor found in step 2: 36503865295478130758755327213624903058483920561 Found probable prime factor of 47 digits: 36503865295478130758755327213624903058483920561 Probable prime cofactor 1423801300523414982742214232334802997389942436426180599813692010039144526423143680899283 has 88 digits

(52·10²⁰⁰+11)/9 = 5(7)₁₉₉9_<201> = 3 · C201
C201 = P37 · P41 · P123
P37 = 8075439109054338741026365424340286769_<37>
P41 = 46072334646769181132736381886218495737461_<41>
P123 = 517646417427145438243223197026762870951002843055646221049761620790442362955715502310129467442320445073950466702993889063677_<123>

Number: 57779_200 N=192592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593 ( 201 digits) SNFS difficulty: 201 digits. Divisors found: r1=8075439109054338741026365424340286769 r2=46072334646769181132736381886218495737461 r3=517646417427145438243223197026762870951002843055646221049761620790442362955715502310129467442320445073950466702993889063677 Version: Total time: 724.79 hours. Scaled time: 1437.98 units (timescale=1.984). Factorization parameters were as follows: n: 192592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593 m: 10000000000000000000000000000000000000000 deg: 5 c5: 52 c0: 11 skew: 0.73 type: snfs lss: 1 rlim: 16100000 alim: 16100000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 16100000/16100000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [8050000, 15150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2550504 x 2550752 Total sieving time: 724.79 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,16100000,16100000,29,29,56,56,2.6,2.6,100000 total time: 724.79 hours. --------- CPU info (if available) ----------

May 28, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / May 28, 2009
(56·10¹⁵⁸+61)/9 = 6(2)₁₅₇9_<159> = 37 · 113 · 223 · 557 · 3527 · 45653899 · C139
C139 = P45 · P95
P45 = 124878684080187282583724105767405939123035029_<45>
P95 = 59584547392283647789639726101806207148068690320073897315957313077500509015687698972674356372107_<95>

Number: n N=7440839869861936630058067963126918327949604224644175519468827650795213963955279495313110552543506489514537808067602830238665387271519536103 ( 139 digits) SNFS difficulty: 160 digits. Divisors found: Thu May 28 06:18:05 2009 prp45 factor: 124878684080187282583724105767405939123035029 Thu May 28 06:18:05 2009 prp95 factor: 59584547392283647789639726101806207148068690320073897315957313077500509015687698972674356372107 Thu May 28 06:18:05 2009 elapsed time 01:01:35 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 26.13 hours. Scaled time: 69.22 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_2_157_9 n: 7440839869861936630058067963126918327949604224644175519468827650795213963955279495313110552543506489514537808067602830238665387271519536103 m: 40000000000000000000000000000000 deg: 5 c5: 875 c0: 976 skew: 1.02 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1700000, 3337129) Primes: RFBsize:243539, AFBsize:243630, largePrimes:13449259 encountered Relations: rels:12430495, finalFF:445077 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1223572 hash collisions in 13440933 relations Msieve: matrix is 683080 x 683328 (182.1 MB) Total sieving time: 25.77 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.4,2.4,100000 total time: 26.13 hours. --------- CPU info (if available) ----------

(56·10²⁰⁰+61)/9 = 6(2)₁₉₉9_<201> = 37 · C200
C200 = P60 · P67 · P73
P60 = 481076100939208673226663917864223084277575369417353564944939_<60>
P67 = 8545755976691122629091211724599067284274966594431886983135257852967_<67>
P73 = 4090529449389188605462156151123695237619192394785337828054066652466473909_<73>

Number: n N=16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817 ( 200 digits) SNFS difficulty: 201 digits. Divisors found: Thu May 28 09:36:48 2009 prp60 factor: 481076100939208673226663917864223084277575369417353564944939 Thu May 28 09:36:48 2009 prp67 factor: 8545755976691122629091211724599067284274966594431886983135257852967 Thu May 28 09:36:48 2009 prp73 factor: 4090529449389188605462156151123695237619192394785337828054066652466473909 Thu May 28 09:36:48 2009 elapsed time 14:35:01 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 41.52 hours. Scaled time: 83.69 units (timescale=2.016). Factorization parameters were as follows: name: KA_6_2_199_9 n: 16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817 m: 10000000000000000000000000000000000000000 deg: 5 c5: 56 c0: 61 skew: 1.02 type: snfs lss: 1 rlim: 16000000 alim: 16000000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved special-q in [8000000, 15599990) Primes: RFBsize:1031130, AFBsize:1029484, largePrimes:35216489 encountered Relations: rels:33331588, finalFF:1260378 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 4741784 hash collisions in 38635157 relations Msieve: matrix is 2987116 x 2987364 (816.9 MB) Total sieving time: 40.75 hours. Total relation processing time: 0.76 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,56,56,2.6,2.6,100000 total time: 41.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.70 BogoMIPS).

(56·10¹⁵⁵+61)/9 = 6(2)₁₅₄9_<156> = 23 · 37 · 251 · 27017372954252618111623_<23> · C129
C129 = P48 · P81
P48 = 177021412931799064494121309758465332060558628233_<48>
P81 = 609078564125640040336170484954565150827351856308547897231649778954045702279685131_<81>

Number: n N=107819948007992181599739919757114454654783869201061103982701027821480434645578678954568874887411940205225700015025344436526903523 ( 129 digits) SNFS difficulty: 156 digits. Divisors found: r1=177021412931799064494121309758465332060558628233 (pp48) r2=609078564125640040336170484954565150827351856308547897231649778954045702279685131 (pp81) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 16.46 hours. Scaled time: 43.60 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_2_154_9 n: 107819948007992181599739919757114454654783869201061103982701027821480434645578678954568874887411940205225700015025344436526903523 m: 10000000000000000000000000000000 deg: 5 c5: 56 c0: 61 skew: 1.02 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1500000, 2400001) Primes: RFBsize:216816, AFBsize:216332, largePrimes:13126010 encountered Relations: rels:12952716, finalFF:813070 Max relations in full relation-set: 28 Initial matrix: 433214 x 813070 with sparse part having weight 92819045. Pruned matrix : 311917 x 314147 with weight 40066358. Total sieving time: 15.57 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.49 hours. Total square root time: 0.13 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000 total time: 16.46 hours. --------- CPU info (if available) ----------

(56·10¹⁵⁶-11)/9 = 6(2)₁₅₅1_<157> = 23 · 17083343429_<11> · 77944473401_<11> · 479005799717307893_<18> · C117
C117 = P42 · P76
P42 = 132044681737646078708528335633309997093929_<42>
P76 = 3212164637458965643862477012178193071661944450676327587119744724091254536579_<76>

Number: n N=424149257242190418021587942433779094384856789451403605718656098432866063576129536769017395811084206441250327629328891 ( 117 digits) SNFS difficulty: 158 digits. Divisors found: Thu May 28 21:55:08 2009 prp42 factor: 132044681737646078708528335633309997093929 Thu May 28 21:55:08 2009 prp76 factor: 3212164637458965643862477012178193071661944450676327587119744724091254536579 Thu May 28 21:55:08 2009 elapsed time 00:36:31 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 16.38 hours. Scaled time: 43.74 units (timescale=2.671). Factorization parameters were as follows: name: KA_6_2_155_1 n: 424149257242190418021587942433779094384856789451403605718656098432866063576129536769017395811084206441250327629328891 m: 20000000000000000000000000000000 deg: 5 c5: 35 c0: -22 skew: 0.91 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1500000, 2487227) Primes: RFBsize:216816, AFBsize:216457, largePrimes:11828670 encountered Relations: rels:10501634, finalFF:290618 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 926649 hash collisions in 12226691 relations Msieve: matrix is 545545 x 545793 (146.4 MB) Total sieving time: 16.21 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000 total time: 16.38 hours. --------- CPU info (if available) ----------

(19·10¹²⁶-7)/3 = 6(3)₁₂₅1_<127> = 23 · 31 · 149 · 2208204383867_<13> · 550564080566484469_<18> · C92
C92 = P39 · P54
P39 = 274896745903554277016688501088576610443_<39>
P54 = 178377390878943326425099144634565645197695200985423067_<54>

Number: n N=49035364295387863925479124276192463882986180905219291115366358148835194378188975727205288681 ( 92 digits) SNFS difficulty: 127 digits. Divisors found: r1=274896745903554277016688501088576610443 (pp39) r2=178377390878943326425099144634565645197695200985423067 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.66 hours. Scaled time: 3.02 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_3_125_1 n: 49035364295387863925479124276192463882986180905219291115366358148835194378188975727205288681 m: 10000000000000000000000000 deg: 5 c5: 190 c0: -7 skew: 0.52 type: snfs lss: 1 rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [350000, 550001) Primes: RFBsize:56543, AFBsize:56408, largePrimes:6577217 encountered Relations: rels:5810183, finalFF:200349 Max relations in full relation-set: 48 Initial matrix: 113018 x 200349 with sparse part having weight 28695026. Pruned matrix : 99364 x 99993 with weight 9200613. Total sieving time: 1.49 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.06 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000 total time: 1.66 hours. --------- CPU info (if available) ----------

May 28, 2009 (4th)

By Serge Batalov / Msieve, GMP-ECM 6.2.3 / May 28, 2009
(19·10¹²⁷-7)/3 = 6(3)₁₂₆1_<128> = 17 · C127
C127 = P35 · P39 · P54
P35 = 12436519676849010829556240379784957_<35>
P39 = 804710243827567182357245316678847272239_<39>
P54 = 372258851965716799664238973288980795787307673603607441_<54>

SNFS difficulty: 129 digits. Divisors found: r1=12436519676849010829556240379784957 (pp35) r2=804710243827567182357245316678847272239 (pp39) r3=372258851965716799664238973288980795787307673603607441 (pp54) Version: Msieve v. 1.41 Total time: 1.53 hours. Scaled time: 4.15 units (timescale=2.712). Factorization parameters were as follows: n: 3725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843 m: 20000000000000000000000000 deg: 5 c5: 475 c0: -56 skew: 0.65 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 135989 x 136232 Total sieving time: 1.39 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,129.000,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 1.53 hours.

(19·10¹⁷³-7)/3 = 6(3)₁₇₂1_<174> = 29 · C173
C173 = P33 · C141
P33 = 122569446876810816963640019353373_<33>
C141 = [178177196815774311635530949428564880269645047657883031777408413802169831219687056745323086331601289126990624176890263158591874451664925011643_<141>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=156145018 Step 1 took 11573ms Step 2 took 11276ms ********** Factor found in step 2: 122569446876810816963640019353373 Found probable prime factor of 33 digits: 122569446876810816963640019353373 Composite cofactor has 141 digits

(19·10¹¹⁰-7)/3 = 6(3)₁₀₉1_<111> = 233 · 4483 · 17387 · C101
C101 = P36 · P66
P36 = 188300054736491233677602258486606213_<36>
P66 = 185196419489526548303620514212561505070907195886173707296562972959_<66>

SNFS difficulty: 111 digits. Divisors found: r1=188300054736491233677602258486606213 (pp36) r2=185196419489526548303620514212561505070907195886173707296562972959 (pp66) Version: Msieve v. 1.41 Total time: 0.46 hours. Scaled time: 1.19 units (timescale=2.575). Factorization parameters were as follows: n: 34872495926880040942521501477836754590113782610902400474116000214661062511721881330962317609600394267 m: 10000000000000000000000 deg: 5 c5: 19 c0: -7 skew: 0.82 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 42818 x 43051 Total sieving time: 0.43 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 0.46 hours.

May 28, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 28, 2009
(56·10¹⁵⁸-11)/9 = 6(2)₁₅₇1_<159> = 3 · 59 · 203211241393631956722915124219_<30> · C128
C128 = P37 · P42 · P49
P37 = 2537899873573280171017705810844700679_<37>
P42 = 939154026293509730665590837625768055750239_<42>
P49 = 7257937322928077535349031612424282545111610115807_<49>

Number: 62221_158 N=17299140354921275130942878961573349031729110752907845125819804596310155375128869475259027043222450254192642083192090196656125767 ( 128 digits) SNFS difficulty: 161 digits. Divisors found: r1=2537899873573280171017705810844700679 r2=939154026293509730665590837625768055750239 r3=7257937322928077535349031612424282545111610115807 Version: Total time: 14.96 hours. Scaled time: 35.76 units (timescale=2.391). Factorization parameters were as follows: n: 17299140354921275130942878961573349031729110752907845125819804596310155375128869475259027043222450254192642083192090196656125767 m: 100000000000000000000000000000000 deg: 5 c5: 14 c0: -275 skew: 1.81 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1600000, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9222390 Max relations in full relation-set: Initial matrix: Pruned matrix : 594313 x 594561 Total sieving time: 13.51 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.73 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,51,51,2.4,2.4,100000 total time: 14.96 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 28, 2009 (2nd)

Factorizations of 633...331 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 28, 2009

By Serge Batalov / PFGW / Mar 27, 2009
(23·10⁹⁵³²⁶+1)/3 = 7(6)₉₅₃₂₅7_<95327> is PRP.

May 27, 2009 (7th)

By Robert Backstrom / GGNFS, Msieve / May 27, 2009
(56·10¹⁴⁷+61)/9 = 6(2)₁₄₆9_<148> = 47 · 257 · 521941369984393_<15> · C129
C129 = P54 · P76
P54 = 465797699955877232314532201968922695556111616869606659_<54>
P76 = 2118826887558452953755045283330372730886493555641871631624937415827575885473_<76>

Number: n N=986944690829397494891842036788406549333195416034921768446440979831502668989069508880958440112596340641488280029932940203142164707 ( 129 digits) SNFS difficulty: 148 digits. Divisors found: r1=465797699955877232314532201968922695556111616869606659 (pp54) r2=2118826887558452953755045283330372730886493555641871631624937415827575885473 (pp76) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 8.43 hours. Scaled time: 21.11 units (timescale=2.504). Factorization parameters were as follows: name: KA_6_2_146_9 n: 986944690829397494891842036788406549333195416034921768446440979831502668989069508880958440112596340641488280029932940203142164707 m: 200000000000000000000000000000 deg: 5 c5: 175 c0: 61 skew: 0.81 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1050000, 2550001) Primes: RFBsize:155805, AFBsize:155723, largePrimes:7753568 encountered Relations: rels:7266143, finalFF:435765 Max relations in full relation-set: 28 Initial matrix: 311594 x 435765 with sparse part having weight 44152462. Pruned matrix : 268454 x 270075 with weight 24701362. Total sieving time: 7.95 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.27 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,28,28,56,56,2.3,2.3,100000 total time: 8.43 hours. --------- CPU info (if available) ----------

(56·10¹⁵⁷+61)/9 = 6(2)₁₅₆9_<158> = 3 · 622385760966490075969_<21> · C137
C137 = P47 · P91
P47 = 14069154013962149347549891861752751330227218953_<47>
P91 = 2368626755962424844786981424733173785115155651413561625293563213425932855103394297861451599_<91>

Number: n N=33324574631226893870084125839523117530322491594485773868792919061646457590097800036857175718446511341481511144550053544984125841384955847 ( 137 digits) SNFS difficulty: 158 digits. Divisors found: Wed May 27 21:27:35 2009 prp47 factor: 14069154013962149347549891861752751330227218953 Wed May 27 21:27:35 2009 prp91 factor: 2368626755962424844786981424733173785115155651413561625293563213425932855103394297861451599 Wed May 27 21:27:35 2009 elapsed time 00:35:53 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 18.00 hours. Scaled time: 47.68 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_2_156_9 n: 33324574631226893870084125839523117530322491594485773868792919061646457590097800036857175718446511341481511144550053544984125841384955847 m: 20000000000000000000000000000000 deg: 5 c5: 175 c0: 61 skew: 0.81 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1500000, 2631523) Primes: RFBsize:216816, AFBsize:216897, largePrimes:12484526 encountered Relations: rels:11502437, finalFF:462209 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1021111 hash collisions in 12654905 relations Msieve: matrix is 530829 x 531077 (142.1 MB) Total sieving time: 17.74 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000 total time: 18.00 hours. --------- CPU info (if available) ----------

May 27, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.3 / May 27, 2009
(73·10²²⁷-1)/9 = 8(1)_227<228> = 7 · 25247 · 3015815141_<10> · 639055693476556840009_<21> · C193
C193 = P35 · C158
P35 = 36279878564912877449080351436751977_<35>
C158 = [65639200136356610405763222555366392184764170615078420676661341059916251862205399722171206761383798033819165310154860533682523793910413983567476004394037283043_<158>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1381633969 Step 1 took 12653ms ********** Factor found in step 1: 36279878564912877449080351436751977 Found probable prime factor of 35 digits: 36279878564912877449080351436751977 Composite cofactor has 158 digits

May 27, 2009 (5th)

By Jo Yeong Uk / GMP-ECM 6.2.3, GGNFS, Msieve v1.39 / May 27, 2009
(56·10¹⁶¹+43)/9 = 6(2)₁₆₀7_<162> = 3³ · 241 · 523 · 21067 · 35373733327_<11> · C141
C141 = P38 · P44 · P60
P38 = 23731097486702355179310475185816769673_<38>
P44 = 68151158133676074312874348411451777745055799_<44>
P60 = 151700972667842036388110214409589568929986947480698193739649_<60>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 245346252744473392713773264651954391624666663016908687743450233882316596771088286439921866261057056653436602715231332271824612453355358691823 (141 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2122690916 Step 1 took 4181ms Step 2 took 2446ms ********** Factor found in step 2: 23731097486702355179310475185816769673 Found probable prime factor of 38 digits: 23731097486702355179310475185816769673 Composite cofactor 10338596977318574636609620997004061760631577234451161306507242896988534078032307853523486220823983674551 has 104 digits Number: 62227_161 N=10338596977318574636609620997004061760631577234451161306507242896988534078032307853523486220823983674551 ( 104 digits) Divisors found: r1=68151158133676074312874348411451777745055799 r2=151700972667842036388110214409589568929986947480698193739649 Version: Total time: 3.99 hours. Scaled time: 9.53 units (timescale=2.387). Factorization parameters were as follows: name: 62227_161 n: 10338596977318574636609620997004061760631577234451161306507242896988534078032307853523486220823983674551 skew: 21347.68 # norm 3.13e+14 c5: 1800 c4: 223241370 c3: -14927947804901 c2: -49922189142606074 c1: 798958580446369787614 c0: -26568840382120456200144 # alpha -5.80 Y1: 51897908579 Y0: -89501759710446812431 # Murphy_E 2.37e-09 # M 1694559806196192336452944050483858266788892742415679960275701010130132314731881164627205298510258439261 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1450001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4950704 Max relations in full relation-set: Initial matrix: Pruned matrix : 243927 x 244175 Polynomial selection time: 0.29 hours. Total sieving time: 3.21 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.99 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(2·10¹⁸⁰+1)/3 = (6)₁₇₉7_<180> = 43 · 659 · 7471369 · 51785777 · C161
C161 = P43 · P119
P43 = 1425608464044510496227793232639877013972121_<43>
P119 = 42652444118965609051628435266578532444132686084908100215479465855804466932393039505383096680112378775502273023323954667_<119>

Number: 66667_180 N=60805685348182876641979890690791410598648830455271886745185368187421994147748888627596878591817404759980073838738634174475982237199577653112470341374075805838707 ( 161 digits) SNFS difficulty: 180 digits. Divisors found: r1=1425608464044510496227793232639877013972121 r2=42652444118965609051628435266578532444132686084908100215479465855804466932393039505383096680112378775502273023323954667 Version: Total time: 60.71 hours. Scaled time: 144.91 units (timescale=2.387). Factorization parameters were as follows: n: 60805685348182876641979890690791410598648830455271886745185368187421994147748888627596878591817404759980073838738634174475982237199577653112470341374075805838707 m: 1000000000000000000000000000000000000 deg: 5 c5: 2 c0: 1 skew: 0.87 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [2600000, 4300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 17440824 Max relations in full relation-set: Initial matrix: Pruned matrix : 1137720 x 1137968 Total sieving time: 55.66 hours. Total relation processing time: 1.55 hours. Matrix solve time: 2.86 hours. Time per square root: 0.64 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,53,53,2.5,2.5,100000 total time: 60.71 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁵⁹+61)/9 = 6(2)₁₅₈9_<160> = 136879 · 1401744473_<10> · 1017640607768771362296572005537507_<34> · C113
C113 = P54 · P60
P54 = 193908127945844596110201403564697754328536812293850033_<54>
P60 = 164342314587529651585996443231840529788907444242118587893377_<60>

Number: 62229_159 N=31867310563954942460860793410742458897721802139714768023254519185323949327123209616553915892182082536506231931441 ( 113 digits) Divisors found: r1=193908127945844596110201403564697754328536812293850033 r2=164342314587529651585996443231840529788907444242118587893377 Version: Total time: 12.13 hours. Scaled time: 28.98 units (timescale=2.389). Factorization parameters were as follows: name: 62229_159 n: 31867310563954942460860793410742458897721802139714768023254519185323949327123209616553915892182082536506231931441 skew: 27061.66 # norm 9.39e+14 c5: 23940 c4: 884131582 c3: -60546641862666 c2: -320075720127746262 c1: 16417652371480033255285 c0: 116175128751983383521569019 # alpha -4.98 Y1: 1292890423231 Y0: -4215443468428684833628 # Murphy_E 7.52e-10 # M 15723322497422548827044109855298921437946360103556637207250493316262810669984092035138974002790496204291964433993 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8284318 Max relations in full relation-set: Initial matrix: Pruned matrix : 452570 x 452818 Polynomial selection time: 1.01 hours. Total sieving time: 10.02 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.43 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000 total time: 12.13 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁶⁵+61)/9 = 6(2)₁₆₄9_<166> = 42701 · 1376939 · 133455793 · C147
C147 = P35 · P113
P35 = 57659426044021677634098200461896179_<35>
P113 = 13752606780688174685773011147018886593941074896390490689917340604450663623768311804047072834136008067972436430313_<113>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 792967413583600859697370064059829457020793249634680186515285950164270324042605059768528085343798618048347992595494171085194377886539401081974474027 (147 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5746488418 Step 1 took 4059ms Step 2 took 2476ms ********** Factor found in step 2: 57659426044021677634098200461896179 Found probable prime factor of 35 digits: 57659426044021677634098200461896179 Probable prime cofactor 13752606780688174685773011147018886593941074896390490689917340604450663623768311804047072834136008067972436430313 has 113 digits

May 27, 2009 (4th)

By Andreas Tete / GGNFS / Msieve v. 1.41 / May 27, 2009
(56·10¹⁷⁰+61)/9 = 6(2)₁₆₉9_<171> = 37 · 67 · 60348354518122561506923_<23> · 50323262668560143510940878296447111_<35> · C110
C110 = P54 · P57
P54 = 311370498917197796572412633772014554924884165146521673_<54>
P57 = 265434460235786313700762170596984220117945146644969782479_<57>

Tue May 26 20:45:04 2009 Msieve v. 1.41 Tue May 26 20:45:04 2009 random seeds: 359fae64 86e64e80 Tue May 26 20:45:04 2009 factoring 82648460313433883981241425769067111639470813131991163858925087068467532014766035327819208292972854598269167367 (110 digits) Tue May 26 20:45:05 2009 searching for 15-digit factors Tue May 26 20:45:07 2009 commencing number field sieve (110-digit input) Tue May 26 20:45:07 2009 R0: -2247903484810375378741 Tue May 26 20:45:07 2009 R1: 231928949747 Tue May 26 20:45:07 2009 A0: -930670227212751277904443904 Tue May 26 20:45:07 2009 A1: 60489629810981899875608 Tue May 26 20:45:07 2009 A2: 3167107438421659766 Tue May 26 20:45:07 2009 A3: -20947784407893 Tue May 26 20:45:07 2009 A4: -515063582 Tue May 26 20:45:07 2009 A5: 1440 Tue May 26 20:45:07 2009 skew 76520.28, size 1.840075e-010, alpha -6.218085, combined = 1.066739e-009 Tue May 26 20:45:07 2009 Tue May 26 20:45:07 2009 commencing relation filtering Tue May 26 20:45:07 2009 commencing duplicate removal, pass 1 Tue May 26 20:46:08 2009 found 565242 hash collisions in 5755946 relations Tue May 26 20:46:25 2009 added 43793 free relations Tue May 26 20:46:25 2009 commencing duplicate removal, pass 2 Tue May 26 20:46:33 2009 found 554761 duplicates and 5244977 unique relations Tue May 26 20:46:33 2009 memory use: 41.3 MB Tue May 26 20:46:33 2009 reading rational ideals above 3080192 Tue May 26 20:46:33 2009 reading algebraic ideals above 3080192 Tue May 26 20:46:33 2009 commencing singleton removal, pass 1 Tue May 26 20:47:24 2009 relations with 0 large ideals: 110843 Tue May 26 20:47:24 2009 relations with 1 large ideals: 727001 Tue May 26 20:47:24 2009 relations with 2 large ideals: 1746135 Tue May 26 20:47:24 2009 relations with 3 large ideals: 1813514 Tue May 26 20:47:24 2009 relations with 4 large ideals: 731433 Tue May 26 20:47:24 2009 relations with 5 large ideals: 72669 Tue May 26 20:47:24 2009 relations with 6 large ideals: 43366 Tue May 26 20:47:24 2009 relations with 7+ large ideals: 16 Tue May 26 20:47:24 2009 5244977 relations and about 5339068 large ideals Tue May 26 20:47:24 2009 commencing singleton removal, pass 2 Tue May 26 20:48:16 2009 found 2357815 singletons Tue May 26 20:48:16 2009 current dataset: 2887162 relations and about 2364014 large ideals Tue May 26 20:48:16 2009 commencing singleton removal, pass 3 Tue May 26 20:48:47 2009 found 586582 singletons Tue May 26 20:48:47 2009 current dataset: 2300580 relations and about 1730089 large ideals Tue May 26 20:48:47 2009 commencing singleton removal, pass 4 Tue May 26 20:49:13 2009 found 178268 singletons Tue May 26 20:49:13 2009 current dataset: 2122312 relations and about 1546296 large ideals Tue May 26 20:49:13 2009 commencing singleton removal, final pass Tue May 26 20:49:38 2009 memory use: 33.4 MB Tue May 26 20:49:38 2009 commencing in-memory singleton removal Tue May 26 20:49:38 2009 begin with 2122312 relations and 1598652 unique ideals Tue May 26 20:49:40 2009 reduce to 1891073 relations and 1363286 ideals in 13 passes Tue May 26 20:49:40 2009 max relations containing the same ideal: 38 Tue May 26 20:49:41 2009 reading rational ideals above 720000 Tue May 26 20:49:41 2009 reading algebraic ideals above 720000 Tue May 26 20:49:41 2009 commencing singleton removal, final pass Tue May 26 20:50:17 2009 keeping 1720791 ideals with weight <= 20, new excess is 192649 Tue May 26 20:50:19 2009 memory use: 47.9 MB Tue May 26 20:50:19 2009 commencing in-memory singleton removal Tue May 26 20:50:20 2009 begin with 1909274 relations and 1720791 unique ideals Tue May 26 20:50:22 2009 reduce to 1881367 relations and 1603481 ideals in 12 passes Tue May 26 20:50:22 2009 max relations containing the same ideal: 20 Tue May 26 20:50:23 2009 removing 233093 relations and 205886 ideals in 27207 cliques Tue May 26 20:50:23 2009 commencing in-memory singleton removal Tue May 26 20:50:23 2009 begin with 1648274 relations and 1603481 unique ideals Tue May 26 20:50:25 2009 reduce to 1629103 relations and 1378053 ideals in 8 passes Tue May 26 20:50:25 2009 max relations containing the same ideal: 20 Tue May 26 20:50:26 2009 removing 173083 relations and 145876 ideals in 27207 cliques Tue May 26 20:50:26 2009 commencing in-memory singleton removal Tue May 26 20:50:26 2009 begin with 1456020 relations and 1378053 unique ideals Tue May 26 20:50:27 2009 reduce to 1443057 relations and 1219015 ideals in 7 passes Tue May 26 20:50:27 2009 max relations containing the same ideal: 20 Tue May 26 20:50:28 2009 relations with 0 large ideals: 14707 Tue May 26 20:50:28 2009 relations with 1 large ideals: 104047 Tue May 26 20:50:28 2009 relations with 2 large ideals: 298920 Tue May 26 20:50:28 2009 relations with 3 large ideals: 443932 Tue May 26 20:50:28 2009 relations with 4 large ideals: 362506 Tue May 26 20:50:28 2009 relations with 5 large ideals: 166027 Tue May 26 20:50:28 2009 relations with 6 large ideals: 45752 Tue May 26 20:50:28 2009 relations with 7+ large ideals: 7166 Tue May 26 20:50:28 2009 commencing 2-way merge Tue May 26 20:50:29 2009 reduce to 869629 relation sets and 645587 unique ideals Tue May 26 20:50:29 2009 commencing full merge Tue May 26 20:50:40 2009 memory use: 50.0 MB Tue May 26 20:50:40 2009 found 408007 cycles, need 379787 Tue May 26 20:50:40 2009 weight of 379787 cycles is about 26862121 (70.73/cycle) Tue May 26 20:50:40 2009 distribution of cycle lengths: Tue May 26 20:50:40 2009 1 relations: 41647 Tue May 26 20:50:40 2009 2 relations: 38819 Tue May 26 20:50:40 2009 3 relations: 38644 Tue May 26 20:50:40 2009 4 relations: 36329 Tue May 26 20:50:40 2009 5 relations: 33244 Tue May 26 20:50:40 2009 6 relations: 29893 Tue May 26 20:50:40 2009 7 relations: 26931 Tue May 26 20:50:40 2009 8 relations: 23810 Tue May 26 20:50:40 2009 9 relations: 20729 Tue May 26 20:50:40 2009 10+ relations: 89741 Tue May 26 20:50:40 2009 heaviest cycle: 20 relations Tue May 26 20:50:40 2009 commencing cycle optimization Tue May 26 20:50:41 2009 start with 2422138 relations Tue May 26 20:50:47 2009 pruned 76207 relations Tue May 26 20:50:47 2009 memory use: 61.9 MB Tue May 26 20:50:47 2009 distribution of cycle lengths: Tue May 26 20:50:47 2009 1 relations: 41647 Tue May 26 20:50:47 2009 2 relations: 39915 Tue May 26 20:50:47 2009 3 relations: 40326 Tue May 26 20:50:47 2009 4 relations: 37675 Tue May 26 20:50:47 2009 5 relations: 34547 Tue May 26 20:50:47 2009 6 relations: 30630 Tue May 26 20:50:47 2009 7 relations: 27402 Tue May 26 20:50:47 2009 8 relations: 24036 Tue May 26 20:50:47 2009 9 relations: 20893 Tue May 26 20:50:47 2009 10+ relations: 82716 Tue May 26 20:50:47 2009 heaviest cycle: 19 relations Tue May 26 20:50:48 2009 RelProcTime: 320 Tue May 26 20:50:48 2009 Tue May 26 20:50:48 2009 commencing linear algebra Tue May 26 20:50:48 2009 read 379787 cycles Tue May 26 20:50:49 2009 cycles contain 1272344 unique relations Tue May 26 20:51:05 2009 read 1272344 relations Tue May 26 20:51:07 2009 using 20 quadratic characters above 134156108 Tue May 26 20:51:15 2009 building initial matrix Tue May 26 20:51:32 2009 memory use: 140.2 MB Tue May 26 20:51:33 2009 read 379787 cycles Tue May 26 20:51:33 2009 matrix is 379562 x 379787 (107.2 MB) with weight 35505175 (93.49/col) Tue May 26 20:51:33 2009 sparse part has weight 25441017 (66.99/col) Tue May 26 20:51:39 2009 filtering completed in 3 passes Tue May 26 20:51:40 2009 matrix is 377431 x 377631 (106.8 MB) with weight 35365680 (93.65/col) Tue May 26 20:51:40 2009 sparse part has weight 25363858 (67.17/col) Tue May 26 20:51:41 2009 read 377631 cycles Tue May 26 20:51:43 2009 matrix is 377431 x 377631 (106.8 MB) with weight 35365680 (93.65/col) Tue May 26 20:51:43 2009 sparse part has weight 25363858 (67.17/col) Tue May 26 20:51:43 2009 saving the first 48 matrix rows for later Tue May 26 20:51:43 2009 matrix is 377383 x 377631 (102.1 MB) with weight 28015668 (74.19/col) Tue May 26 20:51:43 2009 sparse part has weight 24504348 (64.89/col) Tue May 26 20:51:43 2009 matrix includes 64 packed rows Tue May 26 20:51:43 2009 using block size 65536 for processor cache size 3072 kB Tue May 26 20:51:47 2009 commencing Lanczos iteration Tue May 26 20:51:47 2009 memory use: 99.5 MB Tue May 26 21:12:00 2009 lanczos halted after 5969 iterations (dim = 377383) Tue May 26 21:12:01 2009 recovered 29 nontrivial dependencies Tue May 26 21:12:01 2009 BLanczosTime: 1273 Tue May 26 21:12:01 2009 Tue May 26 21:12:01 2009 commencing square root phase Tue May 26 21:12:01 2009 reading relations for dependency 1 Tue May 26 21:12:02 2009 read 188904 cycles Tue May 26 21:12:02 2009 cycles contain 784422 unique relations Tue May 26 21:12:34 2009 read 784422 relations Tue May 26 21:12:38 2009 multiplying 635546 relations Tue May 26 21:14:11 2009 multiply complete, coefficients have about 25.40 million bits Tue May 26 21:14:12 2009 initial square root is modulo 19765799 Tue May 26 21:16:27 2009 sqrtTime: 266 Tue May 26 21:16:27 2009 prp54 factor: 311370498917197796572412633772014554924884165146521673 Tue May 26 21:16:27 2009 prp57 factor: 265434460235786313700762170596984220117945146644969782479 Tue May 26 21:16:27 2009 elapsed time 00:31:23 total time ~ 29 hours

May 27, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / May 27, 2009
(28·10¹⁶⁷+17)/9 = 3(1)₁₆₆3_<168> = 11² · 23 · 9297531860777_<13> · 5625355375946149097_<19> · C133
C133 = P59 · P74
P59 = 54444563831060370474725702212332871377604421032494991959961_<59>
P74 = 39258179248712943472377998594789236506615356188918297471633268441459167679_<74>

Number: 31113_167 N=2137394445997761510395890241674344962098210020617491226246533753230837511777526481868931497067228733273481388043 052545928179953300519 ( 133 digits) SNFS difficulty: 168 digits. Divisors found: r1=54444563831060370474725702212332871377604421032494991959961 (pp59) r2=39258179248712943472377998594789236506615356188918297471633268441459167679 (pp74) Version: Msieve v. 1.41 Total time: 82.07 hours. Scaled time: 64.51 units (timescale=0.786). Factorization parameters were as follows: n: 213739444599776151039589024167434496209821002061749122624653375323083751177752648186893149706722873327348138804305 2545928179953300519 m: 2000000000000000000000000000000000 deg: 5 c5: 175 c0: 34 skew: 0.72 type: snfs lss: 1 rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2250000, 4250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 797429 x 797677 Total sieving time: 76.93 hours. Total relation processing time: 0.26 hours. Matrix solve time: 3.93 hours. Time per square root: 0.95 hours. Prototype def-par.txt line would be: snfs,168.000,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000 total time: 82.07 hours. --------- CPU info (if available) ----------

May 27, 2009 (2th)

By Jo Yeong Uk / GMP-ECM / May 27, 2009
(56·10¹⁵³+43)/9 = 6(2)₁₅₂7_<154> = 13 · 123289 · 213417229 · 137435871258200903_<18> · C123
C123 = P36 · P87
P36 = 207855748749177702475903581228065689_<36>
P87 = 636775313135541920644661803313139569186068666649278705384340856517311504776930805506077_<87>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 132357409496780157389212183926742930693742441984686316735685449045612894064896546327354637730958479189188077024805444692053 (123 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=6068088808 Step 1 took 9885ms Step 2 took 4900ms ********** Factor found in step 2: 207855748749177702475903581228065689 Found probable prime factor of 36 digits: 207855748749177702475903581228065689 Probable prime cofactor 636775313135541920644661803313139569186068666649278705384340856517311504776930805506077 has 87 digits

May 27, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / May 27, 2009
(56·10¹⁶⁸-11)/9 = 6(2)₁₆₇1_<169> = 33409 · 682183 · 251073507463_<12> · 21345376764104279543479_<23> · C125
C125 = P37 · P89
P37 = 2010311494190430198841667490889357457_<37>
P89 = 25340377371216548369200872625377112559349060405814187929776061184010278109483909816007387_<89>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1641621734 Step 1 took 11410ms Step 2 took 5745ms ********** Factor found in step 2: 2010311494190430198841667490889357457 Found probable prime factor of 37 digits: 2010311494190430198841667490889357457 Probable prime cofactor 25340377371216548369200872625377112559349060405814187929776061184010278109483909816007387 has 89 digits

May 26, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / May 26, 2009
(56·10¹⁴⁸+61)/9 = 6(2)₁₄₇9_<149> = 3 · 877 · 1543 · 588079 · 22446283 · 9580622869530879653_<19> · C111
C111 = P51 · P60
P51 = 289514970278927942159258952609383815151082133561159_<51>
P60 = 418614114873860963119831279688454686719068277729444773205067_<60>

Number: 62229_148 N=121195053026045584142394732863532381780659248901094604117009289059680767354936395953884054694505268254893192653 ( 111 digits) SNFS difficulty: 151 digits. Divisors found: r1=289514970278927942159258952609383815151082133561159 r2=418614114873860963119831279688454686719068277729444773205067 Version: Total time: 9.08 hours. Scaled time: 21.71 units (timescale=2.391). Factorization parameters were as follows: n: 121195053026045584142394732863532381780659248901094604117009289059680767354936395953884054694505268254893192653 m: 1000000000000000000000000000000 deg: 5 c5: 14 c0: 1525 skew: 2.56 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7197933 Max relations in full relation-set: Initial matrix: Pruned matrix : 374222 x 374470 Total sieving time: 8.38 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.28 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 9.08 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(64·10³³³-1)/9 = 7(1)_333<334> = 13 · 4999 · 228777281 · 1541677987_<10> · 1103253089147723_<16> · 897821565552123255197697079_<27> · 3426549570671671064841267094850481127005282543233354557266456990784769879505493_<79> · C191
C191 = P46 · C146
P46 = 1138685703753966317205547366328393186964066889_<46>
C146 = [80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111_<146>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 91407578898967392587495646040927113707134826897259567335187608469947492579148685035563607122524857909977897193250344414103264830313965448959782212407733030637049190216830852599866469613366679 (191 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3772275269 Step 1 took 17355ms Step 2 took 7332ms ********** Factor found in step 2: 1138685703753966317205547366328393186964066889 Found probable prime factor of 46 digits: 1138685703753966317205547366328393186964066889 Composite cofactor 80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111 has 146 digits

(56·10¹⁶⁰+43)/9 = 6(2)₁₅₉7_<161> = 11 · 29 · 89 · 313 · 92791 · 544139 · 6514435771_<10> · 2061956422574897_<16> · C119
C119 = P38 · P81
P38 = 23586179971590229479094783927097020021_<38>
P81 = 437714449894873609652732767202131105370021782154533893534171532886167160496086903_<81>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 10324011791386102959321469009102640141118795635457083329933205374182497205761640135034992221084890050320448802746884963 (119 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3294267125 Step 1 took 3303ms Step 2 took 2127ms ********** Factor found in step 2: 23586179971590229479094783927097020021 Found probable prime factor of 38 digits: 23586179971590229479094783927097020021 Probable prime cofactor 437714449894873609652732767202131105370021782154533893534171532886167160496086903 has 81 digits

(56·10¹⁵⁰+61)/9 = 6(2)₁₄₉9_<151> = 13 · 313 · 2117793157_<10> · 11389628087237_<14> · C125
C125 = P56 · P70
P56 = 45880006269511777788728871269771814767906863056900086357_<56>
P70 = 1381787550307658684570025101538845151921121612343299356704173071667957_<70>

Number: 62229_150 N=63396421471248701503774582755485442858010065898672575389777263502026078279011714548384334671616138564383032169071703329762649 ( 125 digits) SNFS difficulty: 152 digits. Divisors found: r1=45880006269511777788728871269771814767906863056900086357 r2=1381787550307658684570025101538845151921121612343299356704173071667957 Version: Total time: 6.36 hours. Scaled time: 15.22 units (timescale=2.392). Factorization parameters were as follows: n: 63396421471248701503774582755485442858010065898672575389777263502026078279011714548384334671616138564383032169071703329762649 m: 2000000000000000000000000000000 deg: 5 c5: 7 c0: 244 skew: 2.03 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6678090 Max relations in full relation-set: Initial matrix: Pruned matrix : 359761 x 360009 Total sieving time: 5.85 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.27 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 6.36 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁵¹+43)/9 = 6(2)₁₅₀7_<152> = 17 · 23 · 4971942883_<10> · 456814079039621_<15> · C125
C125 = P62 · P63
P62 = 93975190122255146831769552633703935437239278355207260903635149_<62>
P63 = 745572594250544127634375047849152507123131772168599590838274471_<63>

Number: 62227_151 N=70065326294637878981668261731991506218824553413226891366512464715316805317115533774559626960853188454863060360342646504981179 ( 125 digits) SNFS difficulty: 153 digits. Divisors found: r1=93975190122255146831769552633703935437239278355207260903635149 r2=745572594250544127634375047849152507123131772168599590838274471 Version: Total time: 6.94 hours. Scaled time: 16.60 units (timescale=2.391). Factorization parameters were as follows: n: 70065326294637878981668261731991506218824553413226891366512464715316805317115533774559626960853188454863060360342646504981179 m: 2000000000000000000000000000000 deg: 5 c5: 35 c0: 86 skew: 1.20 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1100000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8198304 Max relations in full relation-set: Initial matrix: Pruned matrix : 316651 x 316899 Total sieving time: 6.34 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.21 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000 total time: 6.94 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 26, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / May 26, 2009
(34·10¹⁹³-43)/9 = 3(7)₁₉₂3_<194> = 3³ · 11 · 19² · 79 · 661 · 33889871 · 206690543 · 93566161264769_<14> · 219952497998232711504934775239_<30> · C125
C125 = P41 · P84
P41 = 69424502729465583786896074169319913973389_<41>
P84 = 674206903768606413668523156780015154564362553296911583362292946823897682656330305733_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2671172606 Step 1 took 34040ms Step 2 took 13572ms ********** Factor found in step 2: 69424502729465583786896074169319913973389 Found probable prime factor of 41 digits: 69424502729465583786896074169319913973389 Probable prime cofactor 674206903768606413668523156780015154564362553296911583362292946823897682656330305733 has 84 digits

May 26, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / May 26, 2009
(56·10¹⁵⁸+43)/9 = 6(2)₁₅₇7_<159> = 3 · 11 · 151 · C156
C156 = P51 · P105
P51 = 131335550907515946628289499737357777353323247025711_<51>
P105 = 950763126802695634262216390025909375472382868521848823716068506070698983337343456509688484625876526536779_<105>

Number: n N=124868999041184471648047806988204339197716681160389769661292840100787120654670323544495729926193502352442749793743171226614935224206747385555332575200124869 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: Tue May 26 11:51:07 2009 prp51 factor: 131335550907515946628289499737357777353323247025711 Tue May 26 11:51:07 2009 prp105 factor: 950763126802695634262216390025909375472382868521848823716068506070698983337343456509688484625876526536779 Tue May 26 11:51:07 2009 elapsed time 01:00:34 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 17.56 hours. Scaled time: 46.71 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_157_7 n: 124868999041184471648047806988204339197716681160389769661292840100787120654670323544495729926193502352442749793743171226614935224206747385555332575200124869 m: 100000000000000000000000000000000 deg: 5 c5: 14 c0: 1075 skew: 2.38 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1700000, 2719897) Primes: RFBsize:243539, AFBsize:243744, largePrimes:12847464 encountered Relations: rels:11612917, finalFF:421044 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 910588 hash collisions in 12545435 relations Msieve: matrix is 635285 x 635533 (172.0 MB) Total sieving time: 17.32 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.4,2.4,100000 total time: 17.56 hours. --------- CPU info (if available) ----------

(56·10¹⁵⁷+43)/9 = 6(2)₁₅₆7_<158> = 273028069792489029181_<21> · C138
C138 = P63 · P75
P63 = 320942228218226583907804711929443473075863562997620056114681199_<63>
P75 = 710086662304528289565255283855826775901561463458072754281346535801862830433_<75>

Number: n N=227896795628058710335314314166424003855735536627830620672743604025471001519443133269242576088187366592345094853326988207142020075590129167 ( 138 digits) SNFS difficulty: 158 digits. Divisors found: Tue May 26 12:02:33 2009 prp63 factor: 320942228218226583907804711929443473075863562997620056114681199 Tue May 26 12:02:33 2009 prp75 factor: 710086662304528289565255283855826775901561463458072754281346535801862830433 Tue May 26 12:02:33 2009 elapsed time 01:12:33 (Msieve 1.39 - dependency 8) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 17.54 hours. Scaled time: 46.45 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_2_156_7 n: 227896795628058710335314314166424003855735536627830620672743604025471001519443133269242576088187366592345094853326988207142020075590129167 m: 20000000000000000000000000000000 deg: 5 c5: 175 c0: 43 skew: 0.76 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1500000, 2549171) Primes: RFBsize:216816, AFBsize:217001, largePrimes:12428958 encountered Relations: rels:11393794, finalFF:436268 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1006927 hash collisions in 12751827 relations Msieve: matrix is 518804 x 519052 (138.8 MB) Total sieving time: 17.27 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000 total time: 17.54 hours. --------- CPU info (if available) ----------

(29·10¹⁶⁹-11)/9 = 3(2)₁₆₈1_<170> = 739 · 20375213 · 761841315115219_<15> · C145
C145 = P38 · P107
P38 = 30185337815716905249692358934686648943_<38>
P107 = 93056846468806542487059667457037413274973699346875535788608105484856824239552996076515719745447019284007559_<107>

Number: n N=2808952346726228286607349592413192856250276838617066864027465513158652213003638652734864016020646324259579957110275941513825532651046513191360137 ( 145 digits) SNFS difficulty: 171 digits. Divisors found: Tue May 26 23:55:05 2009 prp38 factor: 30185337815716905249692358934686648943 Tue May 26 23:55:05 2009 prp107 factor: 93056846468806542487059667457037413274973699346875535788608105484856824239552996076515719745447019284007559 Tue May 26 23:55:05 2009 elapsed time 01:59:15 (Msieve 1.39 - dependency 8) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 65.82 hours. Scaled time: 166.07 units (timescale=2.523). Factorization parameters were as follows: name: KA_3_2_168_1 n: 2808952346726228286607349592413192856250276838617066864027465513158652213003638652734864016020646324259579957110275941513825532651046513191360137 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: -110 skew: 1.31 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 6278801) Primes: RFBsize:348513, AFBsize:349112, largePrimes:17921984 encountered Relations: rels:17899366, finalFF:670524 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2434863 hash collisions in 20268295 relations Msieve: matrix is 879292 x 879540 (232.6 MB) Total sieving time: 64.98 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 65.82 hours. --------- CPU info (if available) ----------

May 26, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve 1.41 / May 26, 2009
(16·10¹⁹⁷-7)/9 = 1(7)_197<198> = 3 · C197
C197 = P52 · P146
P52 = 2492719882705008579729261285974409303651590046350993_<52>
P146 = 23772931595889256247702401807095568187613434909292752523159600299070459234751820679071565671109595402287192339846210282361233657325888516506821963_<146>

Number: big197 N=59259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 ( 197 digits) SNFS difficulty: 198 digits. Divisors found: r1=2492719882705008579729261285974409303651590046350993 (pp52) r2=23772931595889256247702401807095568187613434909292752523159600299070459234751820679071565671109595402287192339846210282361233657325888516506821963 (pp146) Version: Msieve v. 1.41 Total time: 619.58 hours. Scaled time: 1231.72 units (timescale=1.988). Factorization parameters were as follows: n: 59259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 m: 2000000000000000000000000000000000000000 deg: 5 c5: 50 c0: -7 skew: 0.67 type: snfs lss: 1 rlim: 14100000 alim: 14100000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 14100000/14100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [7050000, 15550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2584336 x 2584584 Total sieving time: 607.29 hours. Total relation processing time: 0.42 hours. Matrix solve time: 11.22 hours. Time per square root: 0.65 hours. Prototype def-par.txt line would be: snfs,198.000,5,0,0,0,0,0,0,0,0,14100000,14100000,28,28,55,55,2.5,2.5,100000 total time: 619.58 hours. --------- CPU info (if available) ----------

(16·10¹⁸⁹-7)/9 = 1(7)_189<190> = 97 · 565257584232221_<15> · 2894757784480057_<16> · 313874266742039388275321127723139_<33> · C125
C125 = P49 · P76
P49 = 9641915714367601914559833623585613291763136575081_<49>
P76 = 3701076555786604628832541036576489067616431031951291380827268989656764182967_<76>

Number: 477 N=35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327 ( 125 digits) Divisors found: r1=9641915714367601914559833623585613291763136575081 (pp49) r2=3701076555786604628832541036576489067616431031951291380827268989656764182967 (pp76) Version: Msieve v. 1.41 Total time: 65.61 hours. Scaled time: 130.43 units (timescale=1.988). Factorization parameters were as follows: # Murphy_E = 1.630694e-10, selected by Jeff Gilchrist n: 35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327 Y0: -1168519198374191872033102 Y1: 20511124710263 c0: -352577385070769488032860696085 c1: 39647842142184592470391721 c2: 173482975072407524037 c3: -2569127795806573 c4: -3778907800 c5: 16380 skew: 207212.3 type: gnfs # selected mechanically rlim: 7000000 alim: 7000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3500000, 6900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 915481 x 915729 Total sieving time: 64.15 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.15 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,7000000,7000000,27,27,52,52,2.5,2.5,100000 total time: 65.61 hours. --------- CPU info (if available) ----------

May 26, 2009 (3rd)

By Andreas Tete / GGNFS, Msieve v. 1.41 / May 26, 2009
(56·10¹⁶⁷+43)/9 = 6(2)₁₆₆7_<168> = 3 · 17 · 107 · 272993143283568505766291_<24> · 202190630619170096698842510247_<30> · C112
C112 = P50 · P63
P50 = 12913859117422035067458198332956795125072403023589_<50>
P63 = 159964183537285427027730694363434784194223930354711288637274587_<63>

Tue May 26 06:09:29 2009 Msieve v. 1.41 Tue May 26 06:09:29 2009 random seeds: 1d19d524 4eadf5fa Tue May 26 06:09:29 2009 factoring 2065754930033945216243352113649333727221810688018550046454028316144656706557916899127021556696477554587231232743 (112 digits) Tue May 26 06:09:31 2009 searching for 15-digit factors Tue May 26 06:09:34 2009 commencing number field sieve (112-digit input) Tue May 26 06:09:34 2009 R0: -3625033447227194025530 Tue May 26 06:09:34 2009 R1: 336182944457 Tue May 26 06:09:34 2009 A0: -23268323678036412887177004591 Tue May 26 06:09:34 2009 A1: -262632231566139633823819 Tue May 26 06:09:34 2009 A2: -1655649079234538915 Tue May 26 06:09:34 2009 A3: 84999748352463 Tue May 26 06:09:34 2009 A4: 390639850 Tue May 26 06:09:34 2009 A5: 3300 Tue May 26 06:09:34 2009 skew 116347.62, size 1.254584e-010, alpha -7.586029, combined = 8.633661e-010 Tue May 26 06:09:34 2009 Tue May 26 06:09:34 2009 commencing relation filtering Tue May 26 06:09:34 2009 commencing duplicate removal, pass 1 Tue May 26 06:11:31 2009 found 435423 hash collisions in 8143655 relations Tue May 26 06:11:58 2009 added 58787 free relations Tue May 26 06:11:58 2009 commencing duplicate removal, pass 2 Tue May 26 06:12:53 2009 found 339672 duplicates and 7862769 unique relations Tue May 26 06:12:53 2009 memory use: 41.3 MB Tue May 26 06:12:53 2009 reading rational ideals above 3604480 Tue May 26 06:12:53 2009 reading algebraic ideals above 3604480 Tue May 26 06:12:53 2009 commencing singleton removal, pass 1 Tue May 26 06:14:40 2009 relations with 0 large ideals: 138250 Tue May 26 06:14:40 2009 relations with 1 large ideals: 1038561 Tue May 26 06:14:40 2009 relations with 2 large ideals: 2734154 Tue May 26 06:14:40 2009 relations with 3 large ideals: 2897588 Tue May 26 06:14:40 2009 relations with 4 large ideals: 997490 Tue May 26 06:14:40 2009 relations with 5 large ideals: 0 Tue May 26 06:14:40 2009 relations with 6 large ideals: 56726 Tue May 26 06:14:40 2009 relations with 7+ large ideals: 0 Tue May 26 06:14:40 2009 7862769 relations and about 7636607 large ideals Tue May 26 06:14:40 2009 commencing singleton removal, pass 2 Tue May 26 06:16:31 2009 found 3528605 singletons Tue May 26 06:16:31 2009 current dataset: 4334164 relations and about 3416603 large ideals Tue May 26 06:16:31 2009 commencing singleton removal, pass 3 Tue May 26 06:17:39 2009 found 719044 singletons Tue May 26 06:17:39 2009 current dataset: 3615120 relations and about 2653573 large ideals Tue May 26 06:17:39 2009 commencing singleton removal, pass 4 Tue May 26 06:18:28 2009 found 189682 singletons Tue May 26 06:18:28 2009 current dataset: 3425438 relations and about 2460057 large ideals Tue May 26 06:18:28 2009 commencing singleton removal, final pass Tue May 26 06:19:21 2009 memory use: 66.6 MB Tue May 26 06:19:21 2009 commencing in-memory singleton removal Tue May 26 06:19:21 2009 begin with 3425438 relations and 2588466 unique ideals Tue May 26 06:19:27 2009 reduce to 3051772 relations and 2208065 ideals in 15 passes Tue May 26 06:19:27 2009 max relations containing the same ideal: 19 Tue May 26 06:19:28 2009 reading rational ideals above 720000 Tue May 26 06:19:28 2009 reading algebraic ideals above 720000 Tue May 26 06:19:28 2009 commencing singleton removal, final pass Tue May 26 06:20:24 2009 keeping 2576865 ideals with weight <= 20, new excess is 231323 Tue May 26 06:20:28 2009 memory use: 90.6 MB Tue May 26 06:20:28 2009 commencing in-memory singleton removal Tue May 26 06:20:29 2009 begin with 3066465 relations and 2576865 unique ideals Tue May 26 06:20:32 2009 reduce to 3048947 relations and 2487838 ideals in 8 passes Tue May 26 06:20:32 2009 max relations containing the same ideal: 20 Tue May 26 06:20:36 2009 removing 749279 relations and 602892 ideals in 146387 cliques Tue May 26 06:20:36 2009 commencing in-memory singleton removal Tue May 26 06:20:36 2009 begin with 2299668 relations and 2487838 unique ideals Tue May 26 06:20:40 2009 reduce to 2192609 relations and 1771961 ideals in 9 passes Tue May 26 06:20:40 2009 max relations containing the same ideal: 20 Tue May 26 06:20:42 2009 removing 568468 relations and 422081 ideals in 146387 cliques Tue May 26 06:20:42 2009 commencing in-memory singleton removal Tue May 26 06:20:42 2009 begin with 1624141 relations and 1771961 unique ideals Tue May 26 06:20:44 2009 reduce to 1525450 relations and 1244801 ideals in 10 passes Tue May 26 06:20:44 2009 max relations containing the same ideal: 19 Tue May 26 06:20:45 2009 removing 81649 relations and 69335 ideals in 12314 cliques Tue May 26 06:20:45 2009 commencing in-memory singleton removal Tue May 26 06:20:46 2009 begin with 1443801 relations and 1244801 unique ideals Tue May 26 06:20:47 2009 reduce to 1441089 relations and 1172727 ideals in 5 passes Tue May 26 06:20:47 2009 max relations containing the same ideal: 18 Tue May 26 06:20:47 2009 relations with 0 large ideals: 25242 Tue May 26 06:20:47 2009 relations with 1 large ideals: 159541 Tue May 26 06:20:47 2009 relations with 2 large ideals: 390608 Tue May 26 06:20:47 2009 relations with 3 large ideals: 466073 Tue May 26 06:20:47 2009 relations with 4 large ideals: 287778 Tue May 26 06:20:47 2009 relations with 5 large ideals: 92935 Tue May 26 06:20:47 2009 relations with 6 large ideals: 17392 Tue May 26 06:20:47 2009 relations with 7+ large ideals: 1520 Tue May 26 06:20:47 2009 commencing 2-way merge Tue May 26 06:20:50 2009 reduce to 897524 relation sets and 629162 unique ideals Tue May 26 06:20:50 2009 commencing full merge Tue May 26 06:21:03 2009 memory use: 45.4 MB Tue May 26 06:21:03 2009 found 429073 cycles, need 393362 Tue May 26 06:21:03 2009 weight of 393362 cycles is about 27680407 (70.37/cycle) Tue May 26 06:21:03 2009 distribution of cycle lengths: Tue May 26 06:21:03 2009 1 relations: 39720 Tue May 26 06:21:03 2009 2 relations: 37268 Tue May 26 06:21:03 2009 3 relations: 39791 Tue May 26 06:21:03 2009 4 relations: 38591 Tue May 26 06:21:03 2009 5 relations: 36964 Tue May 26 06:21:03 2009 6 relations: 34142 Tue May 26 06:21:03 2009 7 relations: 31447 Tue May 26 06:21:03 2009 8 relations: 28300 Tue May 26 06:21:03 2009 9 relations: 24566 Tue May 26 06:21:03 2009 10+ relations: 82573 Tue May 26 06:21:03 2009 heaviest cycle: 17 relations Tue May 26 06:21:03 2009 commencing cycle optimization Tue May 26 06:21:04 2009 start with 2426704 relations Tue May 26 06:21:12 2009 pruned 76457 relations Tue May 26 06:21:12 2009 memory use: 62.3 MB Tue May 26 06:21:12 2009 distribution of cycle lengths: Tue May 26 06:21:12 2009 1 relations: 39720 Tue May 26 06:21:12 2009 2 relations: 38302 Tue May 26 06:21:12 2009 3 relations: 41621 Tue May 26 06:21:12 2009 4 relations: 39935 Tue May 26 06:21:12 2009 5 relations: 38536 Tue May 26 06:21:12 2009 6 relations: 35428 Tue May 26 06:21:12 2009 7 relations: 32474 Tue May 26 06:21:12 2009 8 relations: 28730 Tue May 26 06:21:12 2009 9 relations: 24690 Tue May 26 06:21:12 2009 10+ relations: 73926 Tue May 26 06:21:12 2009 heaviest cycle: 17 relations Tue May 26 06:21:13 2009 RelProcTime: 530 Tue May 26 06:21:13 2009 Tue May 26 06:21:13 2009 commencing linear algebra Tue May 26 06:21:13 2009 read 393362 cycles Tue May 26 06:21:14 2009 cycles contain 1279167 unique relations Tue May 26 06:21:37 2009 read 1279167 relations Tue May 26 06:21:40 2009 using 20 quadratic characters above 134216012 Tue May 26 06:21:50 2009 building initial matrix Tue May 26 06:22:17 2009 memory use: 144.5 MB Tue May 26 06:22:19 2009 read 393362 cycles Tue May 26 06:22:20 2009 matrix is 393137 x 393362 (112.2 MB) with weight 37544918 (95.45/col) Tue May 26 06:22:20 2009 sparse part has weight 26262120 (66.76/col) Tue May 26 06:22:29 2009 filtering completed in 3 passes Tue May 26 06:22:30 2009 matrix is 391430 x 391630 (111.9 MB) with weight 37438270 (95.60/col) Tue May 26 06:22:30 2009 sparse part has weight 26207109 (66.92/col) Tue May 26 06:22:31 2009 read 391630 cycles Tue May 26 06:22:32 2009 matrix is 391430 x 391630 (111.9 MB) with weight 37438270 (95.60/col) Tue May 26 06:22:32 2009 sparse part has weight 26207109 (66.92/col) Tue May 26 06:22:32 2009 saving the first 48 matrix rows for later Tue May 26 06:22:32 2009 matrix is 391382 x 391630 (107.1 MB) with weight 29862902 (76.25/col) Tue May 26 06:22:32 2009 sparse part has weight 25728315 (65.70/col) Tue May 26 06:22:32 2009 matrix includes 64 packed rows Tue May 26 06:22:32 2009 using block size 65536 for processor cache size 3072 kB Tue May 26 06:22:36 2009 commencing Lanczos iteration Tue May 26 06:22:36 2009 memory use: 104.1 MB Tue May 26 06:51:48 2009 lanczos halted after 6191 iterations (dim = 391380) Tue May 26 06:51:49 2009 recovered 28 nontrivial dependencies Tue May 26 06:51:49 2009 BLanczosTime: 1836 Tue May 26 06:51:49 2009 Tue May 26 06:51:49 2009 commencing square root phase Tue May 26 06:51:49 2009 reading relations for dependency 1 Tue May 26 06:51:49 2009 read 195890 cycles Tue May 26 06:51:50 2009 cycles contain 791224 unique relations Tue May 26 06:52:40 2009 read 791224 relations Tue May 26 06:52:45 2009 multiplying 638908 relations Tue May 26 06:54:36 2009 multiply complete, coefficients have about 26.49 million bits Tue May 26 06:54:37 2009 initial square root is modulo 40454321 Tue May 26 06:57:24 2009 reading relations for dependency 2 Tue May 26 06:57:25 2009 read 195289 cycles Tue May 26 06:57:25 2009 cycles contain 789633 unique relations Tue May 26 06:58:16 2009 read 789633 relations Tue May 26 06:58:22 2009 multiplying 638022 relations Tue May 26 07:00:12 2009 multiply complete, coefficients have about 26.45 million bits Tue May 26 07:00:13 2009 initial square root is modulo 39556393 Tue May 26 07:02:57 2009 sqrtTime: 668 Tue May 26 07:02:57 2009 prp50 factor: 12913859117422035067458198332956795125072403023589 Tue May 26 07:02:57 2009 prp63 factor: 159964183537285427027730694363434784194223930354711288637274587 Tue May 26 07:02:57 2009 elapsed time 00:53:28

May 26, 2009 (2nd)

By Sinkiti Sibata / Msieve / May 26, 2009
(56·10¹⁴²+61)/9 = 6(2)₁₄₁9_<143> = 3⁴ · 19 · 131 · 42419329483_<11> · 87525447502071318703_<20> · C107
C107 = P38 · P70
P38 = 44872549100086381398779792036441672819_<38>
P70 = 1852493621640036569971842416827656964494493099561502515079759713220051_<70>

Number: 62229_142 N=83126110994639384502124993651960889801899443839353934431248268695470043758248670095884805167694367492493769 ( 107 digits) SNFS difficulty: 143 digits. Divisors found: r1=44872549100086381398779792036441672819 (pp38) r2=1852493621640036569971842416827656964494493099561502515079759713220051 (pp70) Version: Msieve-1.40 Total time: 6.74 hours. Scaled time: 17.29 units (timescale=2.564). Factorization parameters were as follows: name: 62229_142 n: 83126110994639384502124993651960889801899443839353934431248268695470043758248670095884805167694367492493769 m: 20000000000000000000000000000 deg: 5 c5: 175 c0: 61 skew: 0.81 type: snfs lss: 1 rlim: 1740000 alim: 1740000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1740000/1740000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [870000, 1770001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 282609 x 282857 Total sieving time: 6.74 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,143.000,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000 total time: 6.74 hours. --------- CPU info (if available) ----------

(56·10¹⁴⁹+43)/9 = 6(2)₁₄₈7_<150> = 3 · 503 · 521 · 8099537 · 1053083254675877_<16> · C122
C122 = P39 · P84
P39 = 150749794589437620706289474468020105961_<39>
P84 = 615515402049415406036097417507594704876193733951431676017316119220986881163077938187_<84>

Number: 62227_149 N=92788820425584484372450631418906503883926540579412767808945265882752439664813153845210701883662809020035395189181148232707 ( 122 digits) SNFS difficulty: 151 digits. Divisors found: r1=150749794589437620706289474468020105961 (pp39) r2=615515402049415406036097417507594704876193733951431676017316119220986881163077938187 (pp84) Version: Msieve-1.40 Total time: 15.19 hours. Scaled time: 31.57 units (timescale=2.078). Factorization parameters were as follows: name: 62227_149 n: 92788820425584484372450631418906503883926540579412767808945265882752439664813153845210701883662809020035395189181148232707 m: 1000000000000000000000000000000 deg: 5 c5: 28 c0: 215 skew: 1.50 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 370302 x 370550 Total sieving time: 14.54 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.47 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 15.19 hours. --------- CPU info (if available) ----------

May 26, 2009

Factorizations of 811...11 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 25, 2009 (8th)

By Erik Branger / GGNFS, Msieve / May 25, 2009
(56·10¹¹⁴+61)/9 = 6(2)₁₁₃9_<115> = 13 · 17 · 53 · 16391888269_<11> · C101
C101 = P43 · P58
P43 = 6330526609647274115237024207116463641404217_<43>
P58 = 5119276068573292810156043341228585529455167728488587180721_<58>

Number: 62229_114 N=32407713374233713689381067581298315293249215778887709800371510988289185758861020536966163909590500457 ( 101 digits) SNFS difficulty: 116 digits. Divisors found: r1=6330526609647274115237024207116463641404217 (pp43) r2=5119276068573292810156043341228585529455167728488587180721 (pp58) Version: Msieve v. 1.41 Total time: 1.42 hours. Scaled time: 1.24 units (timescale=0.873). Factorization parameters were as follows: n: 32407713374233713689381067581298315293249215778887709800371510988289185758861020536966163909590500457 m: 100000000000000000000000 deg: 5 c5: 28 c0: 305 skew: 1.61 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [305000, 505001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 59031 x 59258 Total sieving time: 1.38 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116.000,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000 total time: 1.42 hours. --------- CPU info (if available) ----------

(56·10¹⁵²+61)/9 = 6(2)₁₅₁9_<153> = 37 · 11186507 · C145
C145 = P32 · P45 · P68
P32 = 28942433849206367671246614943001_<32>
P45 = 595936129032331976442960402461375031323194639_<45>
P68 = 87159459781777493595426241904554628150888105525357079878608434976229_<68>

Number: 62229_152 N=1503312590500038735667605340685597105228362778194910781070160400991731987189282303834147407838462606496989347686173782112398161179071967399369331 ( 145 digits) SNFS difficulty: 153 digits. Divisors found: r1=28942433849206367671246614943001 (pp32) r2=595936129032331976442960402461375031323194639 (pp45) r3=87159459781777493595426241904554628150888105525357079878608434976229 (pp68) Version: Msieve v. 1.41 Total time: 23.52 hours. Scaled time: 21.85 units (timescale=0.929). Factorization parameters were as follows: n: 1503312590500038735667605340685597105228362778194910781070160400991731987189282303834147407838462606496989347686173782112398161179071967399369331 m: 2000000000000000000000000000000 deg: 5 c5: 175 c0: 61 skew: 0.81 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1300000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 417187 x 417435 Total sieving time: 22.71 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.56 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 23.52 hours. --------- CPU info (if available) ----------

May 25, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / May 25, 2009
(2·10¹⁷⁶+1)/3 = (6)₁₇₅7_<176> = 891423615315154872538304147_<27> · C149
C149 = P46 · P104
P46 = 1103614510810071915219795913454294436119696473_<46>
P104 = 67765274784633510325405809275250340559244879028941434970319872358880286167373422167498357591651212673457_<104>

Number: 66667_176 N=74786740581353412957536483508702404864499831989498538968548097789732163315742538650870690452878548195480134264825891327689726788458624388437703617161 ( 149 digits) SNFS difficulty: 176 digits. Divisors found: r1=1103614510810071915219795913454294436119696473 r2=67765274784633510325405809275250340559244879028941434970319872358880286167373422167498357591651212673457 Version: Total time: 41.82 hours. Scaled time: 99.56 units (timescale=2.381). Factorization parameters were as follows: n: 74786740581353412957536483508702404864499831989498538968548097789732163315742538650870690452878548195480134264825891327689726788458624388437703617161 m: 100000000000000000000000000000000000 deg: 5 c5: 20 c0: 1 skew: 0.55 type: snfs lss: 1 rlim: 6800000 alim: 6800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6800000/6800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3400000, 6200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 17375629 Max relations in full relation-set: Initial matrix: Pruned matrix : 1270401 x 1270648 Total sieving time: 35.56 hours. Total relation processing time: 2.43 hours. Matrix solve time: 3.67 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000 total time: 41.82 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(2·10¹⁸³+1)/3 = (6)₁₈₂7_<183> = 83 · 127 · 166561 · C174
C174 = P38 · C136
P38 = 45500165622286770651251939807357753869_<38>
C136 = [8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243_<136>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 379711375471398074234106639718109884265998516506006882170335172843003391956211271054661861198218055599683554842890969670141327812629146543076795651919267864113486694516510167 (174 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=249765663 Step 1 took 18603ms Step 2 took 7278ms ********** Factor found in step 2: 45500165622286770651251939807357753869 Found probable prime factor of 38 digits: 45500165622286770651251939807357753869 Composite cofactor 8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243 has 136 digits

May 25, 2009 (6th)

By Andreas Tete / Msieve 1.41, GGNFS / May 25, 2009
(56·10¹³⁰+61)/9 = 6(2)₁₂₉9_<131> = 3 · 17 · 31 · 383 · 389 · 22362407201_<11> · 93495249169104112307_<20> · C93
C93 = P35 · P58
P35 = 46247980690072474031252763921167863_<35>
P58 = 2731897511788387797568503987411292236154621175780104218527_<58>

Sun May 24 20:20:45 2009 Msieve v. 1.41 Sun May 24 20:20:45 2009 random seeds: 092395d0 b3c8db31 Sun May 24 20:20:45 2009 factoring 126344743372446397853828500971974809042236413069841939570637101725244189122830500998801597801 (93 digits) Sun May 24 20:20:46 2009 searching for 15-digit factors Sun May 24 20:20:48 2009 commencing quadratic sieve (93-digit input) Sun May 24 20:20:48 2009 using multiplier of 1 Sun May 24 20:20:48 2009 using 32kb Intel Core sieve core Sun May 24 20:20:48 2009 sieve interval: 36 blocks of size 32768 Sun May 24 20:20:48 2009 processing polynomials in batches of 6 Sun May 24 20:20:48 2009 using a sieve bound of 1855093 (69412 primes) Sun May 24 20:20:48 2009 using large prime bound of 209625509 (27 bits) Sun May 24 20:20:48 2009 using double large prime bound of 951917611763851 (42-50 bits) Sun May 24 20:20:48 2009 using trial factoring cutoff of 50 bits Sun May 24 20:20:48 2009 polynomial 'A' values have 12 factors Sun May 24 21:50:51 2009 69988 relations (18807 full + 51181 combined from 878512 partial), need 69508 Sun May 24 21:50:52 2009 begin with 897319 relations Sun May 24 21:50:53 2009 reduce to 173296 relations in 11 passes Sun May 24 21:50:53 2009 attempting to read 173296 relations Sun May 24 21:50:55 2009 recovered 173296 relations Sun May 24 21:50:55 2009 recovered 149101 polynomials Sun May 24 21:50:55 2009 attempting to build 69988 cycles Sun May 24 21:50:55 2009 found 69988 cycles in 6 passes Sun May 24 21:50:55 2009 distribution of cycle lengths: Sun May 24 21:50:55 2009 length 1 : 18807 Sun May 24 21:50:55 2009 length 2 : 13230 Sun May 24 21:50:55 2009 length 3 : 12138 Sun May 24 21:50:55 2009 length 4 : 9193 Sun May 24 21:50:55 2009 length 5 : 6597 Sun May 24 21:50:55 2009 length 6 : 4296 Sun May 24 21:50:55 2009 length 7 : 2591 Sun May 24 21:50:55 2009 length 9+: 3136 Sun May 24 21:50:55 2009 largest cycle: 18 relations Sun May 24 21:50:55 2009 matrix is 69412 x 69988 (16.8 MB) with weight 4113021 (58.77/col) Sun May 24 21:50:55 2009 sparse part has weight 4113021 (58.77/col) Sun May 24 21:50:56 2009 filtering completed in 3 passes Sun May 24 21:50:56 2009 matrix is 64767 x 64831 (15.5 MB) with weight 3813493 (58.82/col) Sun May 24 21:50:56 2009 sparse part has weight 3813493 (58.82/col) Sun May 24 21:50:56 2009 saving the first 48 matrix rows for later Sun May 24 21:50:56 2009 matrix is 64719 x 64831 (9.1 MB) with weight 2880785 (44.44/col) Sun May 24 21:50:56 2009 sparse part has weight 1985361 (30.62/col) Sun May 24 21:50:56 2009 matrix includes 64 packed rows Sun May 24 21:50:56 2009 using block size 25932 for processor cache size 3072 kB Sun May 24 21:50:57 2009 commencing Lanczos iteration Sun May 24 21:50:57 2009 memory use: 9.3 MB Sun May 24 21:51:18 2009 lanczos halted after 1025 iterations (dim = 64716) Sun May 24 21:51:18 2009 recovered 14 nontrivial dependencies Sun May 24 21:51:19 2009 prp35 factor: 46247980690072474031252763921167863 Sun May 24 21:51:19 2009 prp58 factor: 2731897511788387797568503987411292236154621175780104218527 Sun May 24 21:51:19 2009 elapsed time 01:30:34

(56·10¹⁴³+61)/9 = 6(2)₁₄₂9_<144> = 37² · 373 · 17957 · 1184131106238803_<16> · 215044693802791697848307401_<27> · C93
C93 = P45 · P48
P45 = 317892978543602332825062735108706473864059569_<45>
P48 = 838281725573898180269529020619937933152992089583_<48>

Sun May 24 20:21:04 2009 Msieve v. 1.41 Sun May 24 20:21:04 2009 random seeds: 122f2e58 cfce9184 Sun May 24 20:21:04 2009 factoring 266483874601357153181251525441014367612362300577944076002637810002542212287393126744496369727 (93 digits) Sun May 24 20:21:05 2009 searching for 15-digit factors Sun May 24 20:21:06 2009 commencing quadratic sieve (93-digit input) Sun May 24 20:21:06 2009 using multiplier of 23 Sun May 24 20:21:06 2009 using 32kb Intel Core sieve core Sun May 24 20:21:06 2009 sieve interval: 36 blocks of size 32768 Sun May 24 20:21:06 2009 processing polynomials in batches of 6 Sun May 24 20:21:06 2009 using a sieve bound of 1923137 (71682 primes) Sun May 24 20:21:06 2009 using large prime bound of 232699577 (27 bits) Sun May 24 20:21:06 2009 using double large prime bound of 1148767303677169 (42-51 bits) Sun May 24 20:21:06 2009 using trial factoring cutoff of 51 bits Sun May 24 20:21:06 2009 polynomial 'A' values have 12 factors Sun May 24 22:15:21 2009 72189 relations (18540 full + 53649 combined from 955622 partial), need 71778 Sun May 24 22:15:22 2009 begin with 974162 relations Sun May 24 22:15:22 2009 reduce to 182692 relations in 10 passes Sun May 24 22:15:22 2009 attempting to read 182692 relations Sun May 24 22:15:24 2009 recovered 182692 relations Sun May 24 22:15:24 2009 recovered 161726 polynomials Sun May 24 22:15:24 2009 attempting to build 72189 cycles Sun May 24 22:15:24 2009 found 72189 cycles in 5 passes Sun May 24 22:15:24 2009 distribution of cycle lengths: Sun May 24 22:15:24 2009 length 1 : 18540 Sun May 24 22:15:24 2009 length 2 : 13035 Sun May 24 22:15:24 2009 length 3 : 12364 Sun May 24 22:15:24 2009 length 4 : 9765 Sun May 24 22:15:24 2009 length 5 : 7042 Sun May 24 22:15:24 2009 length 6 : 4696 Sun May 24 22:15:24 2009 length 7 : 2920 Sun May 24 22:15:24 2009 length 9+: 3827 Sun May 24 22:15:24 2009 largest cycle: 22 relations Sun May 24 22:15:25 2009 matrix is 71682 x 72189 (18.5 MB) with weight 4572493 (63.34/col) Sun May 24 22:15:25 2009 sparse part has weight 4572493 (63.34/col) Sun May 24 22:15:25 2009 filtering completed in 4 passes Sun May 24 22:15:25 2009 matrix is 67624 x 67688 (17.4 MB) with weight 4291973 (63.41/col) Sun May 24 22:15:25 2009 sparse part has weight 4291973 (63.41/col) Sun May 24 22:15:25 2009 saving the first 48 matrix rows for later Sun May 24 22:15:25 2009 matrix is 67576 x 67688 (11.0 MB) with weight 3377687 (49.90/col) Sun May 24 22:15:25 2009 sparse part has weight 2467530 (36.45/col) Sun May 24 22:15:25 2009 matrix includes 64 packed rows Sun May 24 22:15:25 2009 using block size 27075 for processor cache size 3072 kB Sun May 24 22:15:26 2009 commencing Lanczos iteration Sun May 24 22:15:26 2009 memory use: 10.6 MB Sun May 24 22:15:48 2009 lanczos halted after 1069 iterations (dim = 67576) Sun May 24 22:15:48 2009 recovered 18 nontrivial dependencies Sun May 24 22:15:49 2009 prp45 factor: 317892978543602332825062735108706473864059569 Sun May 24 22:15:49 2009 prp48 factor: 838281725573898180269529020619937933152992089583 Sun May 24 22:15:49 2009 elapsed time 01:54:45

(56·10¹⁴⁰+61)/9 = 6(2)₁₃₉9_<141> = 37 · 53 · 89 · 963758813 · 54907861729789_<14> · 460872462819125911_<18> · C96
C96 = P39 · P57
P39 = 978943390360530542658966408125707944647_<39>
P57 = 149326430979469122412950225463477963912388764701360493229_<57>

Sun May 24 22:39:56 2009 Msieve v. 1.41 Sun May 24 22:39:56 2009 random seeds: 06f87b70 c674ec23 Sun May 24 22:39:56 2009 factoring 146182122613479262289613169053058939851336705039243163791190781853654247444845783800423750295163 (96 digits) Sun May 24 22:39:56 2009 searching for 15-digit factors Sun May 24 22:39:58 2009 commencing quadratic sieve (96-digit input) Sun May 24 22:39:58 2009 using multiplier of 43 Sun May 24 22:39:58 2009 using 32kb Intel Core sieve core Sun May 24 22:39:58 2009 sieve interval: 36 blocks of size 32768 Sun May 24 22:39:58 2009 processing polynomials in batches of 6 Sun May 24 22:39:58 2009 using a sieve bound of 2231351 (82021 primes) Sun May 24 22:39:58 2009 using large prime bound of 334702650 (28 bits) Sun May 24 22:39:58 2009 using double large prime bound of 2209970306285550 (43-51 bits) Sun May 24 22:39:58 2009 using trial factoring cutoff of 51 bits Sun May 24 22:39:58 2009 polynomial 'A' values have 13 factors Mon May 25 02:48:05 2009 82159 relations (19904 full + 62255 combined from 1225582 partial), need 82117 Mon May 25 02:48:11 2009 begin with 1245486 relations Mon May 25 02:48:11 2009 reduce to 213522 relations in 10 passes Mon May 25 02:48:11 2009 attempting to read 213522 relations Mon May 25 02:48:14 2009 recovered 213522 relations Mon May 25 02:48:14 2009 recovered 200363 polynomials Mon May 25 02:48:15 2009 attempting to build 82159 cycles Mon May 25 02:48:15 2009 found 82159 cycles in 5 passes Mon May 25 02:48:15 2009 distribution of cycle lengths: Mon May 25 02:48:15 2009 length 1 : 19904 Mon May 25 02:48:15 2009 length 2 : 14671 Mon May 25 02:48:15 2009 length 3 : 13906 Mon May 25 02:48:15 2009 length 4 : 11285 Mon May 25 02:48:15 2009 length 5 : 8474 Mon May 25 02:48:15 2009 length 6 : 5479 Mon May 25 02:48:15 2009 length 7 : 3542 Mon May 25 02:48:15 2009 length 9+: 4898 Mon May 25 02:48:15 2009 largest cycle: 19 relations Mon May 25 02:48:15 2009 matrix is 82021 x 82159 (22.0 MB) with weight 5431070 (66.10/col) Mon May 25 02:48:15 2009 sparse part has weight 5431070 (66.10/col) Mon May 25 02:48:16 2009 filtering completed in 3 passes Mon May 25 02:48:16 2009 matrix is 78309 x 78373 (21.1 MB) with weight 5212730 (66.51/col) Mon May 25 02:48:16 2009 sparse part has weight 5212730 (66.51/col) Mon May 25 02:48:16 2009 saving the first 48 matrix rows for later Mon May 25 02:48:16 2009 matrix is 78261 x 78373 (13.2 MB) with weight 4124874 (52.63/col) Mon May 25 02:48:16 2009 sparse part has weight 2986916 (38.11/col) Mon May 25 02:48:16 2009 matrix includes 64 packed rows Mon May 25 02:48:16 2009 using block size 31349 for processor cache size 3072 kB Mon May 25 02:48:17 2009 commencing Lanczos iteration Mon May 25 02:48:17 2009 memory use: 12.7 MB Mon May 25 02:48:51 2009 lanczos halted after 1240 iterations (dim = 78257) Mon May 25 02:48:51 2009 recovered 15 nontrivial dependencies Mon May 25 02:48:51 2009 prp39 factor: 978943390360530542658966408125707944647 Mon May 25 02:48:51 2009 prp57 factor: 149326430979469122412950225463477963912388764701360493229 Mon May 25 02:48:51 2009 elapsed time 04:08:55

(56·10¹⁴⁹+61)/9 = 6(2)₁₄₈9_<150> = 37 · 367 · 1051 · 341777 · 77367889 · 31670079807843380454722401_<26> · C104
C104 = P36 · P68
P36 = 832195583129323149983272972560380221_<36>
P68 = 62560018490695800182384977161797681356057234677991482841691500909777_<68>

Mon May 25 05:33:46 2009 Msieve v. 1.41 Mon May 25 05:33:46 2009 random seeds: 018af4c8 d7d4be39 Mon May 25 05:33:46 2009 factoring 52062171068445830162659955825043517121841057140092515963953339641548995481118465125414925940886536320717 (104 digits) Mon May 25 05:33:47 2009 searching for 15-digit factors Mon May 25 05:33:48 2009 commencing number field sieve (104-digit input) Mon May 25 05:33:49 2009 R0: -129310016354264376017 Mon May 25 05:33:49 2009 R1: 37729512247 Mon May 25 05:33:49 2009 A0: -12303180889884472428281196 Mon May 25 05:33:49 2009 A1: 6672523770448843233576 Mon May 25 05:33:49 2009 A2: 8027043772154227 Mon May 25 05:33:49 2009 A3: -9727220638494 Mon May 25 05:33:49 2009 A4: -11933922 Mon May 25 05:33:49 2009 A5: 1440 Mon May 25 05:33:49 2009 skew 42751.50, size 6.886428e-010, alpha -5.640437, combined = 2.142178e-009 Mon May 25 05:33:49 2009 Mon May 25 05:33:49 2009 commencing relation filtering Mon May 25 05:33:49 2009 commencing duplicate removal, pass 1 Mon May 25 05:34:50 2009 found 252836 hash collisions in 4403292 relations Mon May 25 05:35:03 2009 added 31659 free relations Mon May 25 05:35:03 2009 commencing duplicate removal, pass 2 Mon May 25 05:35:24 2009 found 229075 duplicates and 4205875 unique relations Mon May 25 05:35:24 2009 memory use: 36.7 MB Mon May 25 05:35:24 2009 reading rational ideals above 2686976 Mon May 25 05:35:24 2009 reading algebraic ideals above 2686976 Mon May 25 05:35:24 2009 commencing singleton removal, pass 1 Mon May 25 05:36:10 2009 relations with 0 large ideals: 105708 Mon May 25 05:36:10 2009 relations with 1 large ideals: 667887 Mon May 25 05:36:10 2009 relations with 2 large ideals: 1524536 Mon May 25 05:36:10 2009 relations with 3 large ideals: 1433892 Mon May 25 05:36:10 2009 relations with 4 large ideals: 443789 Mon May 25 05:36:10 2009 relations with 5 large ideals: 0 Mon May 25 05:36:10 2009 relations with 6 large ideals: 30063 Mon May 25 05:36:10 2009 relations with 7+ large ideals: 0 Mon May 25 05:36:10 2009 4205875 relations and about 4232833 large ideals Mon May 25 05:36:10 2009 commencing singleton removal, pass 2 Mon May 25 05:36:57 2009 found 1957334 singletons Mon May 25 05:36:57 2009 current dataset: 2248541 relations and about 1850202 large ideals Mon May 25 05:36:57 2009 commencing singleton removal, pass 3 Mon May 25 05:37:22 2009 found 469164 singletons Mon May 25 05:37:22 2009 current dataset: 1779377 relations and about 1341428 large ideals Mon May 25 05:37:22 2009 commencing singleton removal, final pass Mon May 25 05:37:42 2009 memory use: 33.3 MB Mon May 25 05:37:42 2009 commencing in-memory singleton removal Mon May 25 05:37:42 2009 begin with 1779377 relations and 1378143 unique ideals Mon May 25 05:37:44 2009 reduce to 1436060 relations and 1023327 ideals in 17 passes Mon May 25 05:37:44 2009 max relations containing the same ideal: 15 Mon May 25 05:37:44 2009 reading rational ideals above 100000 Mon May 25 05:37:44 2009 reading algebraic ideals above 100000 Mon May 25 05:37:44 2009 commencing singleton removal, final pass Mon May 25 05:38:06 2009 keeping 1311028 ideals with weight <= 25, new excess is 105073 Mon May 25 05:38:08 2009 memory use: 46.3 MB Mon May 25 05:38:08 2009 commencing in-memory singleton removal Mon May 25 05:38:08 2009 begin with 1436466 relations and 1311028 unique ideals Mon May 25 05:38:10 2009 reduce to 1418531 relations and 1291094 ideals in 14 passes Mon May 25 05:38:10 2009 max relations containing the same ideal: 25 Mon May 25 05:38:11 2009 relations with 0 large ideals: 3714 Mon May 25 05:38:11 2009 relations with 1 large ideals: 36679 Mon May 25 05:38:11 2009 relations with 2 large ideals: 154974 Mon May 25 05:38:11 2009 relations with 3 large ideals: 345255 Mon May 25 05:38:11 2009 relations with 4 large ideals: 428854 Mon May 25 05:38:11 2009 relations with 5 large ideals: 297777 Mon May 25 05:38:11 2009 relations with 6 large ideals: 120870 Mon May 25 05:38:11 2009 relations with 7+ large ideals: 30408 Mon May 25 05:38:11 2009 commencing 2-way merge Mon May 25 05:38:13 2009 reduce to 793834 relation sets and 666539 unique ideals Mon May 25 05:38:13 2009 ignored 142 oversize relation sets Mon May 25 05:38:13 2009 commencing full merge Mon May 25 05:38:26 2009 memory use: 51.8 MB Mon May 25 05:38:26 2009 found 348548 cycles, need 336739 Mon May 25 05:38:26 2009 weight of 336739 cycles is about 23875670 (70.90/cycle) Mon May 25 05:38:26 2009 distribution of cycle lengths: Mon May 25 05:38:26 2009 1 relations: 37628 Mon May 25 05:38:26 2009 2 relations: 36630 Mon May 25 05:38:26 2009 3 relations: 35577 Mon May 25 05:38:26 2009 4 relations: 32071 Mon May 25 05:38:26 2009 5 relations: 28916 Mon May 25 05:38:26 2009 6 relations: 25285 Mon May 25 05:38:26 2009 7 relations: 21939 Mon May 25 05:38:26 2009 8 relations: 18742 Mon May 25 05:38:26 2009 9 relations: 16541 Mon May 25 05:38:26 2009 10+ relations: 83410 Mon May 25 05:38:26 2009 heaviest cycle: 23 relations Mon May 25 05:38:26 2009 commencing cycle optimization Mon May 25 05:38:27 2009 start with 2248490 relations Mon May 25 05:38:33 2009 pruned 62276 relations Mon May 25 05:38:33 2009 memory use: 57.9 MB Mon May 25 05:38:33 2009 distribution of cycle lengths: Mon May 25 05:38:33 2009 1 relations: 37628 Mon May 25 05:38:33 2009 2 relations: 37508 Mon May 25 05:38:33 2009 3 relations: 36957 Mon May 25 05:38:33 2009 4 relations: 32991 Mon May 25 05:38:33 2009 5 relations: 29754 Mon May 25 05:38:33 2009 6 relations: 25609 Mon May 25 05:38:33 2009 7 relations: 22241 Mon May 25 05:38:33 2009 8 relations: 18838 Mon May 25 05:38:33 2009 9 relations: 16417 Mon May 25 05:38:33 2009 10+ relations: 78796 Mon May 25 05:38:33 2009 heaviest cycle: 23 relations Mon May 25 05:38:34 2009 RelProcTime: 240 Mon May 25 05:38:34 2009 Mon May 25 05:38:34 2009 commencing linear algebra Mon May 25 05:38:34 2009 read 336739 cycles Mon May 25 05:38:35 2009 cycles contain 1199734 unique relations Mon May 25 05:38:48 2009 read 1199734 relations Mon May 25 05:38:49 2009 using 20 quadratic characters above 67107320 Mon May 25 05:38:57 2009 building initial matrix Mon May 25 05:39:13 2009 memory use: 131.8 MB Mon May 25 05:39:13 2009 read 336739 cycles Mon May 25 05:39:14 2009 matrix is 336429 x 336739 (95.4 MB) with weight 32260771 (95.80/col) Mon May 25 05:39:14 2009 sparse part has weight 22649350 (67.26/col) Mon May 25 05:39:19 2009 filtering completed in 3 passes Mon May 25 05:39:19 2009 matrix is 333871 x 334071 (94.9 MB) with weight 32048592 (95.93/col) Mon May 25 05:39:19 2009 sparse part has weight 22527086 (67.43/col) Mon May 25 05:39:20 2009 read 334071 cycles Mon May 25 05:39:21 2009 matrix is 333871 x 334071 (94.9 MB) with weight 32048592 (95.93/col) Mon May 25 05:39:21 2009 sparse part has weight 22527086 (67.43/col) Mon May 25 05:39:21 2009 saving the first 48 matrix rows for later Mon May 25 05:39:21 2009 matrix is 333823 x 334071 (91.6 MB) with weight 25399168 (76.03/col) Mon May 25 05:39:21 2009 sparse part has weight 22011721 (65.89/col) Mon May 25 05:39:21 2009 matrix includes 64 packed rows Mon May 25 05:39:21 2009 using block size 65536 for processor cache size 3072 kB Mon May 25 05:39:24 2009 commencing Lanczos iteration Mon May 25 05:39:24 2009 memory use: 89.0 MB Mon May 25 05:55:18 2009 lanczos halted after 5279 iterations (dim = 333823) Mon May 25 05:55:19 2009 recovered 30 nontrivial dependencies Mon May 25 05:55:19 2009 BLanczosTime: 1005 Mon May 25 05:55:19 2009 Mon May 25 05:55:19 2009 commencing square root phase Mon May 25 05:55:19 2009 reading relations for dependency 1 Mon May 25 05:55:20 2009 read 167116 cycles Mon May 25 05:55:20 2009 cycles contain 736925 unique relations Mon May 25 05:55:42 2009 read 736925 relations Mon May 25 05:55:46 2009 multiplying 597656 relations Mon May 25 05:57:16 2009 multiply complete, coefficients have about 22.86 million bits Mon May 25 05:57:17 2009 initial square root is modulo 3683189 Mon May 25 05:59:23 2009 reading relations for dependency 2 Mon May 25 05:59:23 2009 read 166895 cycles Mon May 25 05:59:24 2009 cycles contain 736574 unique relations Mon May 25 05:59:43 2009 read 736574 relations Mon May 25 05:59:47 2009 multiplying 597616 relations Mon May 25 06:01:16 2009 multiply complete, coefficients have about 22.86 million bits Mon May 25 06:01:17 2009 initial square root is modulo 3677743 Mon May 25 06:03:23 2009 reading relations for dependency 3 Mon May 25 06:03:23 2009 read 167360 cycles Mon May 25 06:03:23 2009 cycles contain 737677 unique relations Mon May 25 06:03:32 2009 read 737677 relations Mon May 25 06:03:36 2009 multiplying 598594 relations Mon May 25 06:05:05 2009 multiply complete, coefficients have about 22.89 million bits Mon May 25 06:05:06 2009 initial square root is modulo 3763663 Mon May 25 06:07:13 2009 reading relations for dependency 4 Mon May 25 06:07:13 2009 read 167048 cycles Mon May 25 06:07:13 2009 cycles contain 736390 unique relations Mon May 25 06:07:30 2009 read 736390 relations Mon May 25 06:07:34 2009 multiplying 598082 relations Mon May 25 06:09:02 2009 multiply complete, coefficients have about 22.88 million bits Mon May 25 06:09:03 2009 initial square root is modulo 3720209 Mon May 25 06:11:10 2009 sqrtTime: 951 Mon May 25 06:11:10 2009 prp36 factor: 832195583129323149983272972560380221 Mon May 25 06:11:10 2009 prp68 factor: 62560018490695800182384977161797681356057234677991482841691500909777 Mon May 25 06:11:10 2009 elapsed time 00:37:24 total time 6.5 hours

May 25, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / May 25, 2009
(56·10¹³⁸+43)/9 = 6(2)₁₃₇7_<139> = 11 · 941 · 2081 · 73319904863013559_<17> · C115
C115 = P54 · P62
P54 = 252582742401819496101004032224677833111279988837135163_<54>
P62 = 15597879529518414507388705585990268985508739535035277037248401_<62>

Number: 62227_138 N=3939755187218963168564073683454277537648892061874153338956209989139586816829311362788017536263011469626285242624363 ( 115 digits) SNFS difficulty: 141 digits. Divisors found: r1=252582742401819496101004032224677833111279988837135163 (pp54) r2=15597879529518414507388705585990268985508739535035277037248401 (pp62) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 9.47 hours. Scaled time: 4.48 units (timescale=0.473). Factorization parameters were as follows: name: 62227_138 n: 3939755187218963168564073683454277537648892061874153338956209989139586816829311362788017536263011469626285242624363 m: 10000000000000000000000000000 deg: 5 c5: 14 c0: 1075 skew: 2.38 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1490001) Primes: RFBsize:119758, AFBsize:119798, largePrimes:3500496 encountered Relations: rels:3503621, finalFF:331649 Max relations in full relation-set: 28 Initial matrix: 239623 x 331649 with sparse part having weight 26600511. Pruned matrix : 205538 x 206800 with weight 12852082. Total sieving time: 8.47 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.79 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 9.47 hours. --------- CPU info (if available) ----------

(56·10¹³⁹+43)/9 = 6(2)₁₃₈7_<140> = 36314261237_<11> · C130
C130 = P53 · P78
P53 = 16917846419888696768298044123057919511670201250983773_<53>
P78 = 101279891163629551253563290479520952949599673934425934851975389746050526567827_<78>

Number: 62227_139 N=1713437644129327058688367892522417892364908148116768536706504340616505826625808007270359281141562335294994678738154229856960871271 ( 130 digits) SNFS difficulty: 141 digits. Divisors found: r1=16917846419888696768298044123057919511670201250983773 (pp53) r2=101279891163629551253563290479520952949599673934425934851975389746050526567827 (pp78) Version: Msieve-1.40 Total time: 5.80 hours. Scaled time: 11.89 units (timescale=2.051). Factorization parameters were as follows: name: 62227_139 n: 1713437644129327058688367892522417892364908148116768536706504340616505826625808007270359281141562335294994678738154229856960871271 m: 10000000000000000000000000000 deg: 5 c5: 28 c0: 215 skew: 1.50 type: snfs lss: 1 rlim: 1590000 alim: 1590000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1590000/1590000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [795000, 1495001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 237030 x 237272 Total sieving time: 5.51 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.19 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000 total time: 5.80 hours. --------- CPU info (if available) ----------

(56·10¹³³+61)/9 = 6(2)₁₃₂9_<134> = 3² · 23 · 57791 · 11594399 · C120
C120 = P40 · P81
P40 = 2050093115527204261907231651787933907889_<40>
P81 = 218823083595232013815530432131300867020797233718074161750759354297345178113504747_<81>

Number: 62229_133 N=448607697197019060625892563531944678283091071139362032611439778047028539705459320296028668163660435906071845109662249083 ( 120 digits) SNFS difficulty: 135 digits. Divisors found: r1=2050093115527204261907231651787933907889 (pp40) r2=218823083595232013815530432131300867020797233718074161750759354297345178113504747 (pp81) Version: Msieve-1.40 Total time: 5.02 hours. Scaled time: 12.86 units (timescale=2.564). Factorization parameters were as follows: name: 62229_133 n: 448607697197019060625892563531944678283091071139362032611439778047028539705459320296028668163660435906071845109662249083 m: 400000000000000000000000000 deg: 5 c5: 875 c0: 976 skew: 1.02 type: snfs lss: 1 rlim: 1290000 alim: 1290000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1290000/1290000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [645000, 1395001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 205047 x 205295 Total sieving time: 5.02 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,135.000,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000 total time: 5.02 hours. --------- CPU info (if available) ----------

(56·10¹⁴⁴+43)/9 = 6(2)₁₄₃7_<145> = 11 · 1129 · 7321697527_<10> · 74149919989_<11> · 286114807428707_<15> · C106
C106 = P40 · P67
P40 = 1032081249274106458614747291742945237133_<40>
P67 = 3125231534392205434001538433222177150023095481011878101744560218381_<67>

Number: 62227_144 N=3225492866286339988432275090241219659458968821377202212036109173924177050533883647824390348308870310341673 ( 106 digits) SNFS difficulty: 146 digits. Divisors found: r1=1032081249274106458614747291742945237133 (pp40) r2=3125231534392205434001538433222177150023095481011878101744560218381 (pp67) Version: Msieve-1.40 Total time: 8.53 hours. Scaled time: 17.22 units (timescale=2.019). Factorization parameters were as follows: name: 62227_144 n: 3225492866286339988432275090241219659458968821377202212036109173924177050533883647824390348308870310341673 m: 100000000000000000000000000000 deg: 5 c5: 28 c0: 215 skew: 1.50 type: snfs lss: 1 rlim: 1930000 alim: 1930000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1930000/1930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [965000, 1965001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 295553 x 295788 Total sieving time: 8.07 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.29 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000 total time: 8.53 hours. --------- CPU info (if available) ----------

(56·10¹³¹+61)/9 = 6(2)₁₃₀9_<132> = 37 · 283 · 643883 · C122
C122 = P57 · P66
P57 = 159686308718439159016667656009306239856813271212893922903_<57>
P66 = 577939951522268816742636674750823088926876138623548752575547561151_<66>

Number: 62229_131 N=92289097519504779862952719554869071871120983603499068731655019677004049875514370065206669198915030245941280087690671941353 ( 122 digits) SNFS difficulty: 133 digits. Divisors found: r1=159686308718439159016667656009306239856813271212893922903 (pp57) r2=577939951522268816742636674750823088926876138623548752575547561151 (pp66) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 6.12 hours. Scaled time: 2.90 units (timescale=0.474). Factorization parameters were as follows: name: 62229_131 n: 92289097519504779862952719554869071871120983603499068731655019677004049875514370065206669198915030245941280087690671941353 m: 200000000000000000000000000 deg: 5 c5: 35 c0: 122 skew: 1.28 type: snfs lss: 1 rlim: 1160000 alim: 1160000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1160000/1160000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [580000, 1080001) Primes: RFBsize:90030, AFBsize:89794, largePrimes:2889130 encountered Relations: rels:2764091, finalFF:201528 Max relations in full relation-set: 28 Initial matrix: 179890 x 201528 with sparse part having weight 15605433. Pruned matrix : 172692 x 173655 with weight 11444066. Total sieving time: 5.44 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.50 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1160000,1160000,26,26,47,47,2.3,2.3,50000 total time: 6.12 hours. --------- CPU info (if available) ----------

(56·10¹³⁵+61)/9 = 6(2)₁₃₄9_<136> = 149 · 2769863903_<10> · 121665866875249877_<18> · C108
C108 = P45 · P63
P45 = 209015100514626233074544372015842670379194321_<45>
P63 = 592863072551192271076213234179270899072477314898132518913979571_<63>

Number: 62229_135 N=123917334700697597414242200320681797444203769876573619477198778577783375289171534465147893407700710833216291 ( 108 digits) SNFS difficulty: 136 digits. Divisors found: r1=209015100514626233074544372015842670379194321 (pp45) r2=592863072551192271076213234179270899072477314898132518913979571 (pp63) Version: Msieve-1.40 Total time: 3.83 hours. Scaled time: 9.81 units (timescale=2.564). Factorization parameters were as follows: name: 62229_135 n: 123917334700697597414242200320681797444203769876573619477198778577783375289171534465147893407700710833216291 m: 1000000000000000000000000000 deg: 5 c5: 56 c0: 61 skew: 1.02 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1190001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 171604 x 171852 Total sieving time: 3.83 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 3.83 hours. --------- CPU info (if available) ----------

May 25, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 25, 2009
(56·10¹⁶⁰-11)/9 = 6(2)₁₅₉1_<161> = 269 · 373 · 1230295747861_<13> · C144
C144 = P63 · P81
P63 = 775846871621927753324108755276601243288486937913721807341743493_<63>
P81 = 649679060495355895325070925859546682086034606213142987112835244431188959754868821_<81>

Number: n N=504051466643595019894954236222448362647569780846853338415788166117574360723140988666841004315521289230578075817789845038183606421744841645331753 ( 144 digits) SNFS difficulty: 162 digits. Divisors found: Mon May 25 02:47:00 2009 prp63 factor: 775846871621927753324108755276601243288486937913721807341743493 Mon May 25 02:47:00 2009 prp81 factor: 649679060495355895325070925859546682086034606213142987112835244431188959754868821 Mon May 25 02:47:00 2009 elapsed time 01:07:14 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 24.56 hours. Scaled time: 65.32 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_159_1 n: 504051466643595019894954236222448362647569780846853338415788166117574360723140988666841004315521289230578075817789845038183606421744841645331753 m: 200000000000000000000000000000000 deg: 5 c5: 7 c0: -44 skew: 1.44 type: snfs lss: 1 rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1800000, 3276551) Primes: RFBsize:256726, AFBsize:256192, largePrimes:13666778 encountered Relations: rels:12674729, finalFF:493008 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1249037 hash collisions in 14356305 relations Msieve: matrix is 624633 x 624881 (166.0 MB) Total sieving time: 24.22 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,56,56,2.4,2.4,100000 total time: 24.56 hours. --------- CPU info (if available) ----------

(56·10¹⁶²-11)/9 = 6(2)₁₆₁1_<163> = 197 · 252142207 · 111065768926160413_<18> · C136
C136 = P49 · P87
P49 = 1823252523842627786390503818226391271537327698861_<49>
P87 = 618595406100207642323032126026402169934936034070394900447336655500101739827442920178543_<87>

Number: n N=1127855635409658852402902632598064353581145150105534602459045513277510690669157474826168615022942292427479973569208316215515613457739523 ( 136 digits) SNFS difficulty: 163 digits. Divisors found: Mon May 25 02:50:27 2009 prp49 factor: 1823252523842627786390503818226391271537327698861 Mon May 25 02:50:27 2009 prp87 factor: 618595406100207642323032126026402169934936034070394900447336655500101739827442920178543 Mon May 25 02:50:27 2009 elapsed time 01:11:34 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 23.92 hours. Scaled time: 62.84 units (timescale=2.627). Factorization parameters were as follows: name: KA_6_2_161_1 n: 1127855635409658852402902632598064353581145150105534602459045513277510690669157474826168615022942292427479973569208316215515613457739523 m: 200000000000000000000000000000000 deg: 5 c5: 175 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1900000, 3274757) Primes: RFBsize:269987, AFBsize:270713, largePrimes:13952484 encountered Relations: rels:12951526, finalFF:549074 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1202406 hash collisions in 14619892 relations Msieve: matrix is 621423 x 621671 (167.0 MB) Total sieving time: 23.56 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,56,56,2.4,2.4,100000 total time: 23.92 hours. --------- CPU info (if available) ----------

(56·10¹⁶⁷-11)/9 = 6(2)₁₆₆1_<168> = 3 · 209567 · C162
C162 = P50 · P113
P50 = 19443110822937189264550767307016668556003239123591_<50>
P113 = 50902090040427650194639698198812141669545651810512442623714907082500172503194814420162690721388875673540845020231_<113>

Number: n N=989694977775162155336514849224388417104827608389715019098462102370160413650085210970273981148784910827598846227733409398461625195796129196903173722043105104369521 ( 162 digits) SNFS difficulty: 168 digits. Divisors found: Mon May 25 13:47:58 2009 prp50 factor: 19443110822937189264550767307016668556003239123591 Mon May 25 13:47:58 2009 prp113 factor: 50902090040427650194639698198812141669545651810512442623714907082500172503194814420162690721388875673540845020231 Mon May 25 13:47:58 2009 elapsed time 01:17:42 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 34.31 hours. Scaled time: 91.25 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_166_1 n: 989694977775162155336514849224388417104827608389715019098462102370160413650085210970273981148784910827598846227733409398461625195796129196903173722043105104369521 m: 2000000000000000000000000000000000 deg: 5 c5: 175 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 4166023) Primes: RFBsize:315948, AFBsize:316727, largePrimes:15604488 encountered Relations: rels:14708231, finalFF:619987 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1424982 hash collisions in 15945458 relations Msieve: matrix is 805558 x 805806 (218.3 MB) Total sieving time: 33.73 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 34.31 hours. --------- CPU info (if available) ----------

May 25, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / May 25, 2009
(10²⁰³-7)/3 = (3)₂₀₂1_<203> = 61 · 137458709 · 74987928326523863886652073_<26> · 10610358077968123193638709904195047_<35> · C133
C133 = P46 · P88
P46 = 4587999570650147356774231952309279185249023649_<46>
P88 = 1089010042319197941814674558968741326938785715705358274243860464565699180298897115436301_<88>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=4169885631 Step 1 took 583777ms Step 2 took 152715ms ********** Factor found in step 2: 4587999570650147356774231952309279185249023649 Found probable prime factor of 46 digits: 4587999570650147356774231952309279185249023649 Probable prime cofactor 1089010042319197941814674558968741326938785715705358274243860464565699180298897115436301 has 88 digits

(56·10¹⁹⁹+61)/9 = 6(2)₁₉₈9_<200> = 3 · 23 · 579433 · 312051449 · 81427551415291_<14> · 4489531305364324771_<19> · 39767223830636299661_<20> · C132
C132 = P37 · P96
P37 = 1209584055008769471318521911851364117_<37>
P96 = 283617674035040392384807441800220868385912808582004760099992553834346079760320670717642984524689_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1028574052 Step 1 took 41086ms Step 2 took 15269ms ********** Factor found in step 2: 1209584055008769471318521911851364117 Found probable prime factor of 37 digits: 1209584055008769471318521911851364117 Probable prime cofactor 283617674035040392384807441800220868385912808582004760099992553834346079760320670717642984524689 has 96 digits

May 25, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 25, 2009
(56·10¹⁵⁹+61)/9 = 6(2)₁₅₈9_<160> = 136879 · 1401744473_<10> · C146
C146 = P34 · C113
P34 = 1017640607768771362296572005537507_<34>
C113 = [31867310563954942460860793410742458897721802139714768023254519185323949327123209616553915892182082536506231931441_<113>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2708368817 Step 1 took 9001ms Step 2 took 5336ms ********** Factor found in step 2: 1017640607768771362296572005537507 Found probable prime factor of 34 digits: 1017640607768771362296572005537507 Composite cofactor has 113 digits

(56·10¹⁷⁰+61)/9 = 6(2)₁₆₉9_<171> = 37 · 67 · 60348354518122561506923_<23> · C145
C145 = P35 · C110
P35 = 50323262668560143510940878296447111_<35>
C110 = [82648460313433883981241425769067111639470813131991163858925087068467532014766035327819208292972854598269167367_<110>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3826816614 Step 1 took 9036ms Step 2 took 4981ms ********** Factor found in step 2: 50323262668560143510940878296447111 Found probable prime factor of 35 digits: 50323262668560143510940878296447111 Composite cofactor has 110 digits

(56·10¹⁹⁵+61)/9 = 6(2)₁₉₄9_<196> = 43 · 3182601396073271461249_<22> · C173
C173 = P32 · C142
P32 = 16693093986305324656984769853199_<32>
C142 = [2723691869854779319603026289539237147981460259414140512173402438206782609228973001831820347551262311828517281485882982830362108368597411785553_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3990195945 Step 1 took 10597ms Step 2 took 6004ms ********** Factor found in step 2: 16693093986305324656984769853199 Found probable prime factor of 32 digits: 16693093986305324656984769853199 Composite cofactor has 142 digits

(56·10¹⁹¹+61)/9 = 6(2)₁₉₀9_<192> = 37 · 975849195904534229_<18> · C173
C173 = P30 · P143
P30 = 635681258779264596324193416307_<30>
P143 = 27109510583283492081643976278683612870546015190877688257375898962423467107326967638290646508596450189747001674490682798108581473816237145499039_<143>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3303208364 Step 1 took 10609ms Step 2 took 5792ms ********** Factor found in step 2: 635681258779264596324193416307 Found probable prime factor of 30 digits: 635681258779264596324193416307 Probable prime cofactor has 143 digits

(56·10¹⁰⁷+61)/9 = 6(2)₁₀₆9_<108> = 37 · 379 · 112927 · 55560881 · C91
C91 = P37 · P55
P37 = 2295077568936423863494133074142261789_<37>
P55 = 3081344817769656577369011100621445436455662919402022161_<55>

SNFS difficulty: 108 digits. Divisors found: r1=2295077568936423863494133074142261789 (pp37) r2=3081344817769656577369011100621445436455662919402022161 (pp55) Version: Msieve v. 1.41 Total time: 0.43 hours. Scaled time: 1.27 units (timescale=2.952). Factorization parameters were as follows: n: 7071925373421631420796761079039365887080635651240836510936657912643231821326147396841506029 m: 2000000000000000000000 deg: 5 c5: 175 c0: 61 skew: 0.81 type: snfs lss: 1 rlim: 450000 alim: 450000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [225000, 375001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 40775 x 41003 Total sieving time: 0.40 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,108.000,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.2,2.2,50000 total time: 0.43 hours.

(56·10¹⁰⁹+61)/9 = 6(2)₁₀₈9_<110> = 3 · 59 · 2377 · 71947 · C100
C100 = P40 · P60
P40 = 2824281279310317588227094570203151997417_<40>
P60 = 727817397218189875999836925903135109554540687624630777625599_<60>

SNFS difficulty: 111 digits. Divisors found: r1=2824281279310317588227094570203151997417 (pp40) r2=727817397218189875999836925903135109554540687624630777625599 (pp60) Version: Msieve v. 1.41 Total time: 0.41 hours. Scaled time: 1.22 units (timescale=2.953). Factorization parameters were as follows: n: 2055561049719694884428140807935064724630352561769741255986414432336507158381803421499204389441077783 m: 10000000000000000000000 deg: 5 c5: 28 c0: 305 skew: 1.61 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 48123 x 48349 Total sieving time: 0.38 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 0.41 hours.

May 25, 2009

Factorizations of 622...229 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 24, 2009 (7th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.41 / May 24, 2009
(56·10¹⁵⁵+43)/9 = 6(2)₁₅₄7_<156> = 3 · 59 · 2789452241_<10> · 2996112633712301879539_<22> · C123
C123 = P30 · P35 · P59
P30 = 389870705611988238369726947353_<30>
P35 = 92761963956040897493510077601053423_<35>
P59 = 11630667659548072946415545987059571680567690307767207819271_<59>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2813365054 Step 1 took 11317ms Step 2 took 5645ms ********** Factor found in step 2: 389870705611988238369726947353 Found probable prime factor of 30 digits: 389870705611988238369726947353 Composite cofactor 1078883574219688887059781833004601860775772060817862175000544130711681997737837040792199914633 has 94 digits ---------------------- Sun May 24 19:37:17 2009 Msieve v. 1.41 Sun May 24 19:37:17 2009 random seeds: f1b7c9b4 8e4f20a1 Sun May 24 19:37:17 2009 factoring 1078883574219688887059781833004601860775772060817862175000544130711681997737837040792199914633 (94 digits) Sun May 24 19:37:18 2009 searching for 15-digit factors Sun May 24 19:37:19 2009 commencing quadratic sieve (94-digit input) Sun May 24 19:37:19 2009 using multiplier of 2 Sun May 24 19:37:19 2009 using 32kb Intel Core sieve core Sun May 24 19:37:19 2009 sieve interval: 36 blocks of size 32768 Sun May 24 19:37:19 2009 processing polynomials in batches of 6 Sun May 24 19:37:19 2009 using a sieve bound of 1980947 (74118 primes) Sun May 24 19:37:19 2009 using large prime bound of 255542163 (27 bits) Sun May 24 19:37:19 2009 using double large prime bound of 1359667019806545 (42-51 bits) Sun May 24 19:37:19 2009 using trial factoring cutoff of 51 bits Sun May 24 19:37:19 2009 polynomial 'A' values have 12 factors Sun May 24 22:08:52 2009 74293 relations (17920 full + 56373 combined from 1039979 partial), need 74214 Sun May 24 22:08:53 2009 begin with 1057899 relations Sun May 24 22:08:54 2009 reduce to 194343 relations in 11 passes Sun May 24 22:08:54 2009 attempting to read 194343 relations Sun May 24 22:08:55 2009 recovered 194343 relations Sun May 24 22:08:55 2009 recovered 178893 polynomials Sun May 24 22:08:55 2009 attempting to build 74293 cycles Sun May 24 22:08:55 2009 found 74293 cycles in 5 passes Sun May 24 22:08:55 2009 distribution of cycle lengths: Sun May 24 22:08:55 2009 length 1 : 17920 Sun May 24 22:08:55 2009 length 2 : 12771 Sun May 24 22:08:55 2009 length 3 : 12586 Sun May 24 22:08:55 2009 length 4 : 10058 Sun May 24 22:08:55 2009 length 5 : 7860 Sun May 24 22:08:55 2009 length 6 : 5167 Sun May 24 22:08:55 2009 length 7 : 3339 Sun May 24 22:08:55 2009 length 9+: 4592 Sun May 24 22:08:55 2009 largest cycle: 20 relations Sun May 24 22:08:55 2009 matrix is 74118 x 74293 (19.0 MB) with weight 4686053 (63.08/col) Sun May 24 22:08:55 2009 sparse part has weight 4686053 (63.08/col) Sun May 24 22:08:56 2009 filtering completed in 3 passes Sun May 24 22:08:56 2009 matrix is 70817 x 70881 (18.2 MB) with weight 4498517 (63.47/col) Sun May 24 22:08:56 2009 sparse part has weight 4498517 (63.47/col) Sun May 24 22:08:56 2009 saving the first 48 matrix rows for later Sun May 24 22:08:56 2009 matrix is 70769 x 70881 (10.7 MB) with weight 3460039 (48.81/col) Sun May 24 22:08:56 2009 sparse part has weight 2390791 (33.73/col) Sun May 24 22:08:56 2009 matrix includes 64 packed rows Sun May 24 22:08:56 2009 using block size 28352 for processor cache size 6144 kB Sun May 24 22:08:56 2009 commencing Lanczos iteration Sun May 24 22:08:56 2009 memory use: 10.9 MB Sun May 24 22:09:14 2009 lanczos halted after 1121 iterations (dim = 70765) Sun May 24 22:09:15 2009 recovered 14 nontrivial dependencies Sun May 24 22:09:15 2009 prp35 factor: 92761963956040897493510077601053423 Sun May 24 22:09:15 2009 prp59 factor: 11630667659548072946415545987059571680567690307767207819271 Sun May 24 22:09:15 2009 elapsed time 02:31:58

May 24, 2009 (6th)

By Sinkiti Sibata / GMP-ECM 6.2, Msieve / May 24, 2009
(56·10¹⁷¹+43)/9 = 6(2)₁₇₀7_<172> = 13 · 31 · 866555766780581_<15> · 104333591897662925186183537264500679_<36> · C120
C120 = P30 · P90
P30 = 913359407733730867454204942251_<30>
P90 = 186972652452924239112747207858060766215361741312914837100521197879242145306970573282591041_<90>

Run 38 out of 2318: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3857517126 Step 1 took 44672ms Step 2 took 20984ms ********** Factor found in step 2: 913359407733730867454204942251 Found probable prime factor of 30 digits: 913359407733730867454204942251 Probable prime cofactor 18697265245292423911274720785806076621536174131291483710 0521197879242145306970573282591041 has 90 digits

(56·10¹²¹+43)/9 = 6(2)₁₂₀7_<122> = 220771 · C117
C117 = P49 · P68
P49 = 9837523052183919446566376509856910961364164092149_<49>
P68 = 28649545041019888937504172137615515915556659334640337227186636743213_<68>

Number: 62227_121 N=281840559775614651481499935327657265774138008262961268564359550041546318231208909785353249395175191588669808182334737 ( 117 digits) SNFS difficulty: 123 digits. Divisors found: r1=9837523052183919446566376509856910961364164092149 (pp49) r2=28649545041019888937504172137615515915556659334640337227186636743213 (pp68) Version: Msieve-1.40 Total time: 1.43 hours. Scaled time: 2.99 units (timescale=2.092). Factorization parameters were as follows: name: 62227_121 n: 281840559775614651481499935327657265774138008262961268564359550041546318231208909785353249395175191588669808182334737 m: 2000000000000000000000000 deg: 5 c5: 35 c0: 86 skew: 1.20 type: snfs lss: 1 rlim: 790000 alim: 790000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 790000/790000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [395000, 595001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 77044 x 77272 Total sieving time: 1.38 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,123.000,5,0,0,0,0,0,0,0,0,790000,790000,25,25,46,46,2.2,2.2,50000 total time: 1.43 hours. --------- CPU info (if available) ----------

(56·10¹³¹+43)/9 = 6(2)₁₃₀7_<132> = 3 · 241 · 4974095003_<10> · 12592035475039_<14> · C107
C107 = P36 · P71
P36 = 446751495478926418011405201098840477_<36>
P71 = 30756094804548521464938261943862495082201487416789170131157756023139761_<71>

Number: 62227_131 N=13740331349023691081262371544782048819022677210235262837555319619113317592126935803456752792873718014905997 ( 107 digits) SNFS difficulty: 133 digits. Divisors found: r1=446751495478926418011405201098840477 (pp36) r2=30756094804548521464938261943862495082201487416789170131157756023139761 (pp71) Version: Msieve-1.40 Total time: 2.54 hours. Scaled time: 5.13 units (timescale=2.019). Factorization parameters were as follows: name: 62227_131 n: 13740331349023691081262371544782048819022677210235262837555319619113317592126935803456752792873718014905997 m: 200000000000000000000000000 deg: 5 c5: 35 c0: 86 skew: 1.20 type: snfs lss: 1 rlim: 1160000 alim: 1160000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1160000/1160000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [580000, 880001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 159075 x 159311 Total sieving time: 2.39 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,133.000,5,0,0,0,0,0,0,0,0,1160000,1160000,26,26,47,47,2.3,2.3,50000 total time: 2.54 hours. --------- CPU info (if available) ----------

(56·10¹³⁷+43)/9 = 6(2)₁₃₆7_<138> = 3 · 1019 · 1093 · 185831 · 1994119 · 24351891709373_<14> · C107
C107 = P38 · P70
P38 = 18820540090523760177462888274940089121_<38>
P70 = 1096467833377187138957925392191314902327577642797243965784912605287971_<70>

Number: 62227_137 N=20636116816045076827182019814547604895449093412286731348595867767639030081888155139050751735319042609263491 ( 107 digits) SNFS difficulty: 138 digits. Divisors found: r1=18820540090523760177462888274940089121 (pp38) r2=1096467833377187138957925392191314902327577642797243965784912605287971 (pp70) Version: Msieve-1.40 Total time: 4.85 hours. Scaled time: 9.91 units (timescale=2.045). Factorization parameters were as follows: name: 62227_137 n: 20636116816045076827182019814547604895449093412286731348595867767639030081888155139050751735319042609263491 m: 2000000000000000000000000000 deg: 5 c5: 175 c0: 43 skew: 0.76 type: snfs lss: 1 rlim: 1440000 alim: 1440000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1440000/1440000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [720000, 1320001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 218250 x 218491 Total sieving time: 4.59 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.16 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1440000,1440000,26,26,48,48,2.3,2.3,75000 total time: 4.85 hours. --------- CPU info (if available) ----------

May 24, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 24, 2009
2·10¹⁹⁰-1 = 1(9)_190<191> = 7 · 23 · 151 · 1043761 · C180
C180 = P80 · P101
P80 = 27676127635110233402503730692785558639486036666823955434117813714327581673274833_<80>
P101 = 28478740748702695477340652489819896975660217520497038645376481346236576555545798008200801855853755193_<101>

Number: 19999_190 N=788181263848310569191168289698477608629667806002138500262250231716631429766774029824489209769354914397516489610270580329936650268653863597002338747131096998004045747905232989957769 ( 180 digits) SNFS difficulty: 190 digits. Divisors found: r1=27676127635110233402503730692785558639486036666823955434117813714327581673274833 r2=28478740748702695477340652489819896975660217520497038645376481346236576555545798008200801855853755193 Version: Total time: 128.90 hours. Scaled time: 308.07 units (timescale=2.390). Factorization parameters were as follows: n: 788181263848310569191168289698477608629667806002138500262250231716631429766774029824489209769354914397516489610270580329936650268653863597002338747131096998004045747905232989957769 m: 100000000000000000000000000000000000000 deg: 5 c5: 2 c0: -1 skew: 0.87 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 20445526 Max relations in full relation-set: Initial matrix: Pruned matrix : 1710578 x 1710826 Total sieving time: 118.17 hours. Total relation processing time: 3.65 hours. Matrix solve time: 6.91 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000 total time: 128.90 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹³⁰+43)/9 = 6(2)₁₂₉7_<131> = 11² · C129
C129 = P56 · P73
P56 = 72233322432718414569232836843550578144966505331853321253_<56>
P73 = 7119058409433545234707650257417296676583573298236685291355068311287769679_<73>

Number: 62227_130 N=514233241505968778696051423324150596877869605142332415059687786960514233241505968778696051423324150596877869605142332415059687787 ( 129 digits) SNFS difficulty: 132 digits. Divisors found: r1=72233322432718414569232836843550578144966505331853321253 r2=7119058409433545234707650257417296676583573298236685291355068311287769679 Version: Total time: 1.19 hours. Scaled time: 2.84 units (timescale=2.389). Factorization parameters were as follows: n: 514233241505968778696051423324150596877869605142332415059687786960514233241505968778696051423324150596877869605142332415059687787 m: 200000000000000000000000000 deg: 5 c5: 7 c0: 172 skew: 1.90 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 850001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2835911 Max relations in full relation-set: Initial matrix: Pruned matrix : 148128 x 148376 Total sieving time: 1.03 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 1.19 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹³⁴+43)/9 = 6(2)₁₃₃7_<135> = 3⁴ · 11 · C132
C132 = P54 · P79
P54 = 192604255731103436303710965316098343362792567691761203_<54>
P79 = 3625784053583637817608793557180079376482560388589629390866850398023592021991699_<79>

Number: 62227_134 N=698341439082179822920563661304402045142785883526624267365008105748846489587230327971068711809452550193290934031674772415513156253897 ( 132 digits) SNFS difficulty: 136 digits. Divisors found: r1=192604255731103436303710965316098343362792567691761203 r2=3625784053583637817608793557180079376482560388589629390866850398023592021991699 Version: Total time: 1.86 hours. Scaled time: 4.44 units (timescale=2.390). Factorization parameters were as follows: n: 698341439082179822920563661304402045142785883526624267365008105748846489587230327971068711809452550193290934031674772415513156253897 m: 1000000000000000000000000000 deg: 5 c5: 28 c0: 215 skew: 1.50 type: snfs lss: 1 rlim: 1400000 alim: 1400000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [700000, 1150001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3274434 Max relations in full relation-set: Initial matrix: Pruned matrix : 203984 x 204232 Total sieving time: 1.59 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000 total time: 1.86 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 24, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 24, 2009
(56·10¹⁹⁹+43)/9 = 6(2)₁₉₈7_<200> = 17 · 67 · 302390323 · 54155250493414958844529123_<26> · 5291829120047019899159557464003015689_<37> · C126
C126 = P34 · P93
P34 = 2008749061218436992848565483649771_<34>
P93 = 313820880783536836636772081534716495375043694090733253911265097187774233741468386340143215843_<93>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1829143434 Step 1 took 7572ms Step 2 took 4445ms ********** Factor found in step 2: 2008749061218436992848565483649771 Found probable prime factor of 34 digits: 2008749061218436992848565483649771 Probable prime cofactor has 93 digits

(56·10¹⁸²+43)/9 = 6(2)₁₈₁7_<183> = 3 · 11 · 19 · 763846635731399196931_<21> · C160
C160 = P35 · C125
P35 = 77070395583281942176460981358816319_<35>
C125 = [16857152605764005065047232676396102366871417751924711712204360137910738853018733972405664108283513247694184519411936056181109_<125>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2792916294 Step 1 took 10817ms Step 2 took 5524ms ********** Factor found in step 2: 77070395583281942176460981358816319 Found probable prime factor of 35 digits: 77070395583281942176460981358816319 Composite cofactor has 125 digits

(56·10¹⁶⁷+43)/9 = 6(2)₁₆₆7_<168> = 3 · 17 · 107 · 272993143283568505766291_<24> · C141
C141 = P30 · C112
P30 = 202190630619170096698842510247_<30>
C112 = [2065754930033945216243352113649333727221810688018550046454028316144656706557916899127021556696477554587231232743_<112>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2717518823 Step 1 took 9233ms Step 2 took 4972ms ********** Factor found in step 2: 202190630619170096698842510247 Found probable prime factor of 30 digits: 202190630619170096698842510247 Composite cofactor has 112 digits

(56·10¹⁸⁶+43)/9 = 6(2)₁₈₅7_<187> = 11 · 31 · 20226806889120479159903_<23> · C162
C162 = P35 · P128
P35 = 58045262016572887128888099753888857_<35>
P128 = 15541646783249331782258374772285235272347816600047608549641982111352344802341765058279612308967565859193730460809532798442526657_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3456060348 Step 1 took 10489ms ********** Factor found in step 1: 58045262016572887128888099753888857 Found probable prime factor of 35 digits: 58045262016572887128888099753888857 Probable prime cofactor has 128 digits

(56·10¹⁰⁵+43)/9 = 6(2)₁₀₄7_<106> = 13 · 173 · 191 · C101
C101 = P48 · P53
P48 = 232285334117970032187985184744148944279078916011_<48>
P53 = 62359253040006800401370106387797632463343215746998223_<53>

SNFS difficulty: 106 digits. Divisors found: r1=232285334117970032187985184744148944279078916011 (pp48) r2=62359253040006800401370106387797632463343215746998223 (pp53) Version: Msieve v. 1.41 Total time: 0.30 hours. Scaled time: 0.90 units (timescale=2.943). Factorization parameters were as follows: n: 14485139927745018081851904446705160926024649052219188102733785631827577171522939159049681701983248453 m: 200000000000000000000000000 deg: 4 c4: 35 c0: 43 skew: 1.05 type: snfs lss: 1 rlim: 420000 alim: 420000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 420000/420000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [210000, 310001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 33412 x 33639 Total sieving time: 0.28 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,106.000,4,0,0,0,0,0,0,0,0,420000,420000,25,25,44,44,2.2,2.2,20000 total time: 0.30 hours.

(56·10¹¹¹+43)/9 = 6(2)₁₁₀7_<112> = 13 · 31 · 71 · 5303 · C104
C104 = P47 · P58
P47 = 13897540214212527692645902486242042976664910799_<47>
P58 = 2950683011130204299615480832638819572472845820061038977007_<58>

SNFS difficulty: 113 digits. Divisors found: r1=13897540214212527692645902486242042976664910799 (pp47) r2=2950683011130204299615480832638819572472845820061038977007 (pp58) Version: Msieve v. 1.41 Total time: 0.48 hours. Scaled time: 1.42 units (timescale=2.951). Factorization parameters were as follows: n: 41007235806575725696026815732831110100780693485242177944644714630722910606662210835069365507803866998593 m: 20000000000000000000000 deg: 5 c5: 35 c0: 86 skew: 1.20 type: snfs lss: 1 rlim: 540000 alim: 540000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 540000/540000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [270000, 420001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 43248 x 43476 Total sieving time: 0.45 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,113.000,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000 total time: 0.48 hours.

(56·10¹¹³+43)/9 = 6(2)₁₁₂7_<114> = 3 · 5023929737_<10> · C104
C104 = P36 · P69
P36 = 408348128880194658464406352398206191_<36>
P69 = 101099762660918448367538763269301577394107046179160743691761007449127_<69>

Msieve v. 1.39 Sun May 24 00:22:17 2009 random seeds: 7fbe7db1 de138fc7 factoring 41283898912817818217708765580892400009973986506692143136437221913998955158438237411083324513343488945257 (104 digits) searching for 15-digit factors commencing number field sieve (104-digit input) R0: -100000000000000000000000 R1: 1 A0: 1075 A1: 0 A2: 0 A3: 0 A4: 0 A5: 14 skew 2.38, size 2.597755e-08, alpha -0.612885, combined = 3.186562e-08 commencing square root phase reading relations for dependency 1 read 28696 cycles cycles contain 110948 unique relations read 110948 relations multiplying 85764 relations multiply complete, coefficients have about 1.99 million bits initial square root is modulo 1536515521 Newton iteration failed to converge algebraic square root failed reading relations for dependency 2 read 28880 cycles cycles contain 111389 unique relations read 111389 relations multiplying 86004 relations multiply complete, coefficients have about 2.00 million bits initial square root is modulo 1639707491 reading relations for dependency 3 read 28924 cycles cycles contain 111395 unique relations read 111395 relations multiplying 86186 relations multiply complete, coefficients have about 2.00 million bits initial square root is modulo 1708967971 prp36 factor: 408348128880194658464406352398206191 prp69 factor: 101099762660918448367538763269301577394107046179160743691761007449127 elapsed time 00:30:37

May 24, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / May 24, 2009
(56·10¹⁹⁰-11)/9 = 6(2)₁₈₉1_<191> = C191
C191 = P84 · P108
P84 = 158796307404671877627661739735355205593268234205073217528273831685616486751940901041_<84>
P108 = 391836707283481889552854182532334698780981401663807885131994302605274535384646414268878461059412149522861981_<108>

Number: n N=62222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 191 digits) SNFS difficulty: 192 digits. Divisors found: Sun May 24 06:45:23 2009 prp84 factor: 158796307404671877627661739735355205593268234205073217528273831685616486751940901041 Sun May 24 06:45:23 2009 prp108 factor: 391836707283481889552854182532334698780981401663807885131994302605274535384646414268878461059412149522861981 Sun May 24 06:45:23 2009 elapsed time 03:57:52 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20050930-k8 Total time: 28.54 hours. Scaled time: 57.54 units (timescale=2.016). Factorization parameters were as follows: name: KA_6_2_189_1 n: 62222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 200000000000000000000000000000000000000 deg: 5 c5: 7 c0: -44 skew: 1.44 type: snfs lss: 1 rlim: 11200000 alim: 11200000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 11200000/11200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved special-q in [5600000, 11699990) Primes: RFBsize:738873, AFBsize:739548, largePrimes:20146869 encountered Relations: rels:19495272, finalFF:919837 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3303101 hash collisions in 27644196 relations Msieve: matrix is 1604566 x 1604814 (423.0 MB) Total sieving time: 28.19 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,11200000,11200000,28,28,55,55,2.5,2.5,100000 total time: 28.54 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.70 BogoMIPS).

(56·10¹⁴²+43)/9 = 6(2)₁₄₁7_<143> = 11 · C142
C142 = P47 · P95
P47 = 68896062191871030491723833548784337537918021729_<47>
P95 = 82102887692078698167555009410022945808543510134623548922165046341705571318356455365072720933433_<95>

Number: n N=5656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565657 ( 142 digits) SNFS difficulty: 143 digits. Divisors found: Sun May 24 15:38:08 2009 prp47 factor: 68896062191871030491723833548784337537918021729 Sun May 24 15:38:08 2009 prp95 factor: 82102887692078698167555009410022945808543510134623548922165046341705571318356455365072720933433 Sun May 24 15:38:08 2009 elapsed time 00:23:38 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.91 hours. Scaled time: 8.95 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_2_141_7 n: 5656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565657 m: 20000000000000000000000000000 deg: 5 c5: 175 c0: 43 skew: 0.76 type: snfs lss: 1 rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [900000, 1748963) Primes: RFBsize:135072, AFBsize:135383, largePrimes:5996260 encountered Relations: rels:5238251, finalFF:247066 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 462130 hash collisions in 5983346 relations Msieve: matrix is 270478 x 270726 (72.3 MB) Total sieving time: 4.82 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,56,56,2.3,2.3,100000 total time: 4.91 hours. --------- CPU info (if available) ----------

May 24, 2009 (2nd)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 24, 2009
(16·10¹⁸⁸-7)/9 = 1(7)_188<189> = 3 · 31 · 2069 · 65398169 · 14567926460916274090418321_<26> · C150
C150 = P39 · P112
P39 = 121896753428115558413310315910630311743_<39>
P112 = 7955703066426815166859690188164155329317259808964297303908057957751323028198357087524600604449363008467485722583_<112>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2616785286 Step 1 took 143375ms Step 2 took 39250ms ********** Factor found in step 2: 121896753428115558413310315910630311743 Found probable prime factor of 39 digits: 121896753428115558413310315910630311743 Probable prime cofactor 7955703066426815166859690188164155329317259808964297303908057957751323028198357087524600604449363008467485722583 has 112 digits

May 24, 2009

Factorizations of 622...227 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 23, 2009 (5th)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 23, 2009
(73·10¹⁹⁹-1)/9 = 8(1)_199<200> = 3² · 4386230489_<10> · 261738156131_<12> · C178
C178 = P37 · C142
P37 = 2356059256180297974755710952450611393_<37>
C142 = [3331909097163411490195797154179506593226135680655488427797409658939627839025957996970418820375433315961414173071731590938360326732797877361517_<142>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1302500274 Step 1 took 296422ms ********** Factor found in step 1: 2356059256180297974755710952450611393 Found probable prime factor of 37 digits: 2356059256180297974755710952450611393 Composite cofactor 3331909097163411490195797154179506593226135680655488427797409658939627839025957996970418820375433315961414173071731590938360326732797877361517 has 142 digits

May 23, 2009 (4th)

By Sinkiti Sibata / Msieve, GMP-ECM 6.2 / May 23, 2009
(56·10¹⁴³-11)/9 = 6(2)₁₄₂1_<144> = 3 · 247812371 · 8791047040390906987_<19> · C116
C116 = P53 · P64
P53 = 52096666235637883534522642520955700372141756844560643_<53>
P64 = 1827472048686128722686279854270138033017141595244865854768896437_<64>

Number: 62221_143 N=95205201375358632669691236626623247521905406835492682061039667657362165007206580925633300445028642999687163233128991 ( 116 digits) SNFS difficulty: 146 digits. Divisors found: r1=52096666235637883534522642520955700372141756844560643 (pp53) r2=1827472048686128722686279854270138033017141595244865854768896437 (pp64) Version: Msieve-1.40 Total time: 9.23 hours. Scaled time: 19.31 units (timescale=2.092). Factorization parameters were as follows: name: 62221_143 n: 95205201375358632669691236626623247521905406835492682061039667657362165007206580925633300445028642999687163233128991 m: 100000000000000000000000000000 deg: 5 c5: 14 c0: -275 skew: 1.81 type: snfs lss: 1 rlim: 1910000 alim: 1910000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1910000/1910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [955000, 2055001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 321846 x 322094 Total sieving time: 8.71 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.35 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 9.23 hours. --------- CPU info (if available) ----------

8·10¹⁹³-9 = 7(9)₁₉₂1_<194> = 19 · 281 · 4418326058451689_<16> · 28635389649731171_<17> · 4005799549560803338611269_<25> · C134
C134 = P50 · P84
P50 = 47530447988775454504196992466925654385332702204589_<50>
P84 = 622025352119764712028843316628216948512092949996598055244945354900245093351541822511_<84>

Number: 79991_193 N=29565143646628214552910727018766282005163877039936094266740542090166082984748527095016519714301140410272311793378686931866644647702979 ( 134 digits) Divisors found: r1=47530447988775454504196992466925654385332702204589 (pp50) r2=622025352119764712028843316628216948512092949996598055244945354900245093351541822511 (pp84) Version: Msieve-1.40 Total time: 379.04 hours. Scaled time: 745.57 units (timescale=1.967). Factorization parameters were as follows: name: 79991_193 # Murphy_E = 4.630559e-11, selected by Jeff Gilchrist n: 29565143646628214552910727018766282005163877039936094266740542090166082984748527095016519714301140410272311793378686931866644647702979 Y0: -57543593694049710599247587 Y1: 721718734872989 c0: -90368218213303982886078566019840 c1: 1320429414049798041363608796 c2: 8903540005306081349992 c3: -27320914772887363 c4: -61896802964 c5: 46860 skew: 386466.26 type: gnfs # selected mechanically rlim: 12100000 alim: 12100000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.6 alambda: 2.6 Factor base limits: 12100000/12100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved algebraic special-q in [6050000, 14950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1834899 x 1835147 Total sieving time: 379.04 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,133,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12100000,12100000,28,28,54,54,2.6,2.6,100000 total time: 379.04 hours. --------- CPU info (if available) ----------

(56·10¹⁸⁶-11)/9 = 6(2)₁₈₅1_<187> = 599 · 37158634009449941_<17> · 187078422967358237181929_<24> · 291087023629052324337893_<24> · C121
C121 = P37 · P40 · P45
P37 = 8669942536444244537787894218627299087_<37>
P40 = 2294619415855590800799109639269294659123_<40>
P45 = 258039104434055048772680144104698258424326727_<45>

Run 785 out of 2318: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2397597109 Step 1 took 27125ms Step 2 took 15062ms ********** Factor found in step 2: 2294619415855590800799109639269294659123 Found probable prime factor of 40 digits: 22946194158555908007991096392692946591 23 Probable prime cofactor 258039104434055048772680144104698258424326727msieve has 45 dig its

May 23, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 23, 2009
(56·10¹⁵⁴-11)/9 = 6(2)₁₅₃1_<155> = 1319 · 99588740355980248700009_<23> · C129
C129 = P36 · P94
P36 = 159529283600937361262720079033676357_<36>
P94 = 2969272580593994736122638271517181885182905451818307218893722397054616314597839349595890387543_<94>

Number: 62221_154 N=473685927598066523811321219743107411021072297995390038378143177362996029747199699549590394307377922267919784079276586320766420851 ( 129 digits) SNFS difficulty: 156 digits. Divisors found: r1=159529283600937361262720079033676357 r2=2969272580593994736122638271517181885182905451818307218893722397054616314597839349595890387543 Version: Total time: 12.57 hours. Scaled time: 30.06 units (timescale=2.391). Factorization parameters were as follows: n: 473685927598066523811321219743107411021072297995390038378143177362996029747199699549590394307377922267919784079276586320766420851 m: 10000000000000000000000000000000 deg: 5 c5: 28 c0: -55 skew: 1.14 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8477784 Max relations in full relation-set: Initial matrix: Pruned matrix : 465979 x 466227 Total sieving time: 11.54 hours. Total relation processing time: 0.48 hours. Matrix solve time: 0.45 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 12.57 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 23, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / May 23, 2009
5·10¹⁷¹+9 = 5(0)₁₇₀9_<172> = 67 · 40378193 · 44404164907_<11> · C152
C152 = P59 · P94
P59 = 30861275933615391341234232012900752504190775857799782307643_<59>
P94 = 1348685652951649280820481874144969335193186551718062790432538324525777278141762353767694766939_<94>

Number: n N=41622160083449093835715177170359909547044068164867790126481396040503116696826064618716663968196854901778090190322063002576843971520433247969928483414777 ( 152 digits) SNFS difficulty: 171 digits. Divisors found: Sat May 23 11:46:27 2009 prp59 factor: 30861275933615391341234232012900752504190775857799782307643 Sat May 23 11:46:27 2009 prp94 factor: 1348685652951649280820481874144969335193186551718062790432538324525777278141762353767694766939 Sat May 23 11:46:27 2009 elapsed time 01:19:08 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 45.61 hours. Scaled time: 60.89 units (timescale=1.335). Factorization parameters were as follows: name: KA_5_0_170_9 n: 41622160083449093835715177170359909547044068164867790126481396040503116696826064618716663968196854901778090190322063002576843971520433247969928483414777 m: 10000000000000000000000000000000000 deg: 5 c5: 50 c0: 9 skew: 0.71 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2550000, 5039821) Primes: RFBsize:354971, AFBsize:354121, largePrimes:16733383 encountered Relations: rels:16062335, finalFF:753335 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1755175 hash collisions in 18017048 relations Msieve: matrix is 843918 x 844166 (226.5 MB) Total sieving time: 45.09 hours. Total relation processing time: 0.52 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,28,28,56,56,2.4,2.4,100000 total time: 45.61 hours. --------- CPU info (if available) ----------

May 23, 2009

By Wataru Sakai / Msieve / May 23, 2009
9·10¹⁹⁸+1 = 9(0)₁₉₇1_<199> = 206641 · C194
C194 = P73 · P122
P73 = 1971332907858188412423521352631276953751910015856265250493673622099401969_<73>
P122 = 22093577408287644837009510470494689478804802552229642889751303060701247374764381532930283372837715454765095820414492639969_<122>

Number: 90001_198 N=43553796197269660909500050812762230147937727750059281555935172594015708402495148591034693018326469577673356207141854714214507285582241665497166583591833179281943080027680857138709162266926698961 ( 194 digits) SNFS difficulty: 200 digits. Divisors found: r1=1971332907858188412423521352631276953751910015856265250493673622099401969 r2=22093577408287644837009510470494689478804802552229642889751303060701247374764381532930283372837715454765095820414492639969 Version: Total time: 761.36 hours. Scaled time: 1506.74 units (timescale=1.979). Factorization parameters were as follows: n: 43553796197269660909500050812762230147937727750059281555935172594015708402495148591034693018326469577673356207141854714214507285582241665497166583591833179281943080027680857138709162266926698961 m: 5000000000000000000000000000000000000000 deg: 5 c5: 72 c0: 25 skew: 0.81 type: snfs lss: 1 rlim: 15300000 alim: 15300000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 15300000/15300000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7650000, 15450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3112132 x 3112378 Total sieving time: 761.36 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15300000,15300000,29,29,56,56,2.6,2.6,100000 total time: 761.36 hours. --------- CPU info (if available) ----------

May 22, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / May 22, 2009
(56·10¹⁴⁷-11)/9 = 6(2)₁₄₆1_<148> = 940357975339_<12> · 4396150383764093_<16> · C121
C121 = P40 · P82
P40 = 1008215810246207129612047042208358145051_<40>
P82 = 1492884680420177799347131923818531569599984632006412804870158351516771646036609673_<82>

Number: 62221_147 N=1505149937673979552320836226405694346794312067193454584388061053324185341450817482913564538855807343552377213503203678323 ( 121 digits) SNFS difficulty: 148 digits. Divisors found: r1=1008215810246207129612047042208358145051 r2=1492884680420177799347131923818531569599984632006412804870158351516771646036609673 Version: Total time: 5.64 hours. Scaled time: 13.43 units (timescale=2.380). Factorization parameters were as follows: n: 1505149937673979552320836226405694346794312067193454584388061053324185341450817482913564538855807343552377213503203678323 m: 200000000000000000000000000000 deg: 5 c5: 175 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1500000, 2625001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4957651 Max relations in full relation-set: Initial matrix: Pruned matrix : 378093 x 378341 Total sieving time: 4.93 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.29 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,3000000,3000000,26,26,49,49,2.3,2.3,75000 total time: 5.64 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁸⁹-11)/9 = 6(2)₁₈₈1_<190> = 277 · 25277866982933_<14> · 40398247348837599795974405003_<29> · 54162299091422434499021060679582624167_<38> · C108
C108 = P48 · P61
P48 = 228498442360438340292379803269188129395888720953_<48>
P61 = 1777388907317542637562195901082903456247197584230926518332977_<61>

Number: 62221_189 N=406130596790779999759153981712709459914372909456044656520865406171812435177580766081922259159004770290767081 ( 108 digits) Divisors found: r1=228498442360438340292379803269188129395888720953 r2=1777388907317542637562195901082903456247197584230926518332977 Version: Total time: 6.46 hours. Scaled time: 15.42 units (timescale=2.389). Factorization parameters were as follows: name: 62221_189 n: 406130596790779999759153981712709459914372909456044656520865406171812435177580766081922259159004770290767081 skew: 14032.91 # norm 1.60e+15 c5: 105840 c4: -4277112308 c3: 61395728235004 c2: 1309518592510891537 c1: -4824049825893490081356 c0: -32284824656823243472412025 # alpha -6.61 Y1: 100307285683 Y0: -328703438188208320058 # Murphy_E 1.28e-09 # M 141094203117980261816754148973220116699568804394140714353111345509640429615565396644228123557747415940163645 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 2050001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7208996 Max relations in full relation-set: Initial matrix: Pruned matrix : 348141 x 348389 Polynomial selection time: 0.50 hours. Total sieving time: 4.80 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.25 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 6.46 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁵³-11)/9 = 6(2)₁₅₂1_<154> = 161038333187_<12> · C143
C143 = P64 · P80
P64 = 3363325659726554254219949158081482055226599127679686333139708977_<64>
P80 = 11488076797017378618898480601030100376760617008747621903303917850030785920234079_<80>

Number: 62221_153 N=38638143472317795247537705888526995749935352454153330768119348134235245226490461527992257076379883719605964665915331039200805176564213777627183 ( 143 digits) SNFS difficulty: 156 digits. Divisors found: r1=3363325659726554254219949158081482055226599127679686333139708977 r2=11488076797017378618898480601030100376760617008747621903303917850030785920234079 Version: Total time: 10.66 hours. Scaled time: 25.48 units (timescale=2.390). Factorization parameters were as follows: n: 38638143472317795247537705888526995749935352454153330768119348134235245226490461527992257076379883719605964665915331039200805176564213777627183 m: 10000000000000000000000000000000 deg: 5 c5: 14 c0: -275 skew: 1.81 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8440039 Max relations in full relation-set: Initial matrix: Pruned matrix : 421469 x 421717 Total sieving time: 9.84 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.36 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 10.66 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(2·10¹⁹⁵+1)/3 = (6)₁₉₄7_<195> = 643 · 2267 · 591132392867_<12> · C177
C177 = P38 · P140
P38 = 20445535278979404077682352742063245387_<38>
P140 = 37841034812644230659598583398507678171373442415633054522576738535458043251909493707277588574988992770463156691080518508056734230085009425083_<140>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 773680212255005402213215670718471636322872901200645179715616504990970707569170676906984764825388611905986628614026077579135645235380535252670977400250192112030102091574021842121 (177 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2093518856 Step 1 took 17167ms Step 2 took 7023ms ********** Factor found in step 2: 20445535278979404077682352742063245387 Found probable prime factor of 38 digits: 20445535278979404077682352742063245387 Probable prime cofactor 37841034812644230659598583398507678171373442415633054522576738535458043251909493707277588574988992770463156691080518508056734230085009425083 has 140 digits

(2·10¹⁷²+1)/3 = (6)₁₇₁7_<172> = 19 · 367894099 · C162
C162 = P38 · P125
P38 = 31923954769587137972250253982544737507_<38>
P125 = 29875530881591454506940299770383247214954619398774924636746552858006558949858905691700278509265508508706937584865642995542001_<125>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 953745096581329347038200775768507611618084673281090437797093323267618218445186838896418777162493147199015389346805459313594862392389699576171077293841543738531507 (162 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3322220783 Step 1 took 14428ms Step 2 took 6321ms ********** Factor found in step 2: 31923954769587137972250253982544737507 Found probable prime factor of 38 digits: 31923954769587137972250253982544737507 Probable prime cofactor 29875530881591454506940299770383247214954619398774924636746552858006558949858905691700278509265508508706937584865642995542001 has 125 digits

May 22, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(32·10¹⁶⁹-41)/9 = 3(5)₁₆₈1_<170> = 1613 · 13159 · 116981 · 81326373781_<11> · C147
C147 = P45 · P46 · P57
P45 = 140850378091982090577354915876165350338613087_<45>
P46 = 9786966886270901249855494260133478437860029027_<46>
P57 = 127731302497147884438978142065758231658906688736325985177_<57>

Number: n N=176077343280428722210294933173471602076330384241286510651480244704067065779074311519434584743655131635262384425494570149205597165806500457976278773 ( 147 digits) SNFS difficulty: 171 digits. Divisors found: Fri May 22 13:03:18 2009 prp45 factor: 140850378091982090577354915876165350338613087 Fri May 22 13:03:18 2009 prp46 factor: 9786966886270901249855494260133478437860029027 Fri May 22 13:03:18 2009 prp57 factor: 127731302497147884438978142065758231658906688736325985177 Fri May 22 13:03:18 2009 elapsed time 01:14:43 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 49.74 hours. Scaled time: 132.30 units (timescale=2.660). Factorization parameters were as follows: name: KA_3_5_168_1 n: 176077343280428722210294933173471602076330384241286510651480244704067065779074311519434584743655131635262384425494570149205597165806500457976278773 m: 10000000000000000000000000000000000 deg: 5 c5: 16 c0: -205 skew: 1.67 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 5261749) Primes: RFBsize:348513, AFBsize:348852, largePrimes:17302361 encountered Relations: rels:17224239, finalFF:733473 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1992447 hash collisions in 19178345 relations Msieve: matrix is 783206 x 783454 (206.8 MB) Total sieving time: 49.02 hours. Total relation processing time: 0.72 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 49.74 hours. --------- CPU info (if available) ----------

(56·10¹⁶³-11)/9 = 6(2)₁₆₂1_<164> = 71 · 1212709 · 131517167 · C148
C148 = P34 · P115
P34 = 4653012427420569338623962801251087_<34>
P115 = 1180902142478392291997557302605730893103002830157279589768710079332801129714037937532741668108603105238106040542191_<115>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 5494752344519535146687404917043008612140116501569138078950789948018034611445897276112464677546840828744848284725055003614238674816203386438608111617 (148 digits) Using B1=804000, B2=696806892, polynomial Dickson(3), sigma=562029734 Step 1 took 12495ms Step 2 took 4322ms ********** Factor found in step 2: 4653012427420569338623962801251087 Found probable prime factor of 34 digits: 4653012427420569338623962801251087 Probable prime cofactor 1180902142478392291997557302605730893103002830157279589768710079332801129714037937532741668108603105238106040542191 has 115 digits

(56·10¹⁴¹-11)/9 = 6(2)₁₄₀1_<142> = 19 · 179 · C139
C139 = P54 · P85
P54 = 297263336609650968924047699599162922866765769099232391_<54>
P85 = 6154567475724947698759561455579847624574161601456877967507516611787461722048501183731_<85>

Number: n N=1829527263223234996242935084452285275572544022999771309092097095625469633114443464340553431997125028586363487863046816295860694566957430821 ( 139 digits) SNFS difficulty: 143 digits. Divisors found: r1=297263336609650968924047699599162922866765769099232391 (pp54) r2=6154567475724947698759561455579847624574161601456877967507516611787461722048501183731 (pp85) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 4.94 hours. Scaled time: 13.14 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_140_1 n: 1829527263223234996242935084452285275572544022999771309092097095625469633114443464340553431997125028586363487863046816295860694566957430821 m: 20000000000000000000000000000 deg: 5 c5: 35 c0: -22 skew: 0.91 type: snfs lss: 1 rlim: 1700000 alim: 1700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 1700000/1700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [850000, 1750001) Primes: RFBsize:128141, AFBsize:127925, largePrimes:6368334 encountered Relations: rels:5761128, finalFF:316228 Max relations in full relation-set: 28 Initial matrix: 256132 x 316228 with sparse part having weight 27527715. Pruned matrix : 235172 x 236516 with weight 17145775. Total sieving time: 4.61 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.16 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1700000,1700000,28,28,56,56,2.3,2.3,100000 total time: 4.94 hours. --------- CPU info (if available) ----------

(56·10¹⁴⁶-11)/9 = 6(2)₁₄₅1_<147> = 3² · 1303 · C143
C143 = P63 · P81
P63 = 390636623576473629943499655770771098579496801221468572377451887_<63>
P81 = 135826851857318304777560953992990975187323813555012363701612426250045999154804429_<81>

Number: n N=53058942800564698748377438579536302739167922079152572884985266668561628909543977336251575187364391764494092455207829983987569047686724842007523 ( 143 digits) SNFS difficulty: 148 digits. Divisors found: Fri May 22 20:41:04 2009 prp63 factor: 390636623576473629943499655770771098579496801221468572377451887 Fri May 22 20:41:04 2009 prp81 factor: 135826851857318304777560953992990975187323813555012363701612426250045999154804429 Fri May 22 20:41:04 2009 elapsed time 00:17:27 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 6.71 hours. Scaled time: 17.84 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_145_1 n: 53058942800564698748377438579536302739167922079152572884985266668561628909543977336251575187364391764494092455207829983987569047686724842007523 m: 200000000000000000000000000000 deg: 5 c5: 35 c0: -22 skew: 0.91 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1050000, 2275187) Primes: RFBsize:155805, AFBsize:155618, largePrimes:6972249 encountered Relations: rels:6204110, finalFF:309632 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 625424 hash collisions in 6918126 relations Msieve: matrix is 340345 x 340593 (90.9 MB) Total sieving time: 6.58 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,28,28,56,56,2.3,2.3,100000 total time: 6.71 hours. --------- CPU info (if available) ----------

(5·10¹⁹⁷-11)/3 = 1(6)₁₉₆3_<198> = 7 · C197
C197 = P78 · P119
P78 = 770224136745202272960858853390184251348929602406163327279097423136818113201277_<78>
P119 = 30912461287097049773379532118577710425262942254107754948474511204970390341027073730433138066136695072775834272781147317_<119>

Number: n N=23809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809 ( 197 digits) SNFS difficulty: 198 digits. Divisors found: Fri May 22 20:51:57 2009 prp78 factor: 770224136745202272960858853390184251348929602406163327279097423136818113201277 Fri May 22 20:51:57 2009 prp119 factor: 30912461287097049773379532118577710425262942254107754948474511204970390341027073730433138066136695072775834272781147317 Fri May 22 20:51:57 2009 elapsed time 07:26:51 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 11.89 hours. Scaled time: 23.98 units (timescale=2.016). Factorization parameters were as follows: name: KA_1_6_196_3 n: 23809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809 m: 2000000000000000000000000000000000000000 deg: 5 c5: 125 c0: -88 skew: 0.93 type: snfs lss: 1 rlim: 14300000 alim: 14300000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 14300000/14300000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved special-q in [7150000, 10150057) Primes: RFBsize:928293, AFBsize:926118, largePrimes:36842353 encountered Relations: rels:37172595, finalFF:2021767 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7310015 hash collisions in 43187116 relations Msieve: matrix is 2219007 x 2219255 (603.4 MB) Total sieving time: 11.02 hours. Total relation processing time: 0.87 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,198,5,0,0,0,0,0,0,0,0,14300000,14300000,29,29,56,56,2.5,2.5,100000 total time: 11.89 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.70 BogoMIPS).

May 22, 2009 (3rd)

By Sinkiti Sibata / Msieve, GGNFS, GMP-ECM 6.2
(56·10¹⁴⁰-11)/9 = 6(2)₁₃₉1_<141> = 3 · 137029 · C136
C136 = P36 · P100
P36 = 299406853214567406564359036434117307_<36>
P100 = 5055336135400232322529243029621372499820771506159438962856581567533302079098571471572820157443691769_<100>

Number: 62221_140 N=1513602284242075819041278907438625454519900221175133784873329057406880349469144541720419819216424314615208513580391066178746158896346083 ( 136 digits) SNFS difficulty: 142 digits. Divisors found: r1=299406853214567406564359036434117307 (pp36) r2=5055336135400232322529243029621372499820771506159438962856581567533302079098571471572820157443691769 (pp100) Version: Msieve-1.40 Total time: 7.25 hours. Scaled time: 15.22 units (timescale=2.099). Factorization parameters were as follows: name: 62221_140 n: 1513602284242075819041278907438625454519900221175133784873329057406880349469144541720419819216424314615208513580391066178746158896346083 m: 20000000000000000000000000000 deg: 5 c5: 7 c0: -44 skew: 1.44 type: snfs lss: 1 rlim: 1650000 alim: 1650000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1650000/1650000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [825000, 1725001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 260220 x 260457 Total sieving time: 6.88 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.23 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,142.000,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,48,48,2.3,2.3,100000 total time: 7.25 hours. --------- CPU info (if available) ----------

(56·10¹⁴⁴-11)/9 = 6(2)₁₄₃1_<145> = 467 · 1181321 · 34029929 · 2347379653_<10> · 16006457832853967_<17> · C103
C103 = P41 · P63
P41 = 51446154457445281300092961754341423886897_<41>
P63 = 171462117056719624665955830711633870545040915759347599025265181_<63>

Number: 62221_144 N=8821066557700560914707538403741916445191036516315719696291370434325710113707949441060998120603176233357 ( 103 digits) SNFS difficulty: 146 digits. Divisors found: r1=51446154457445281300092961754341423886897 (pp41) r2=171462117056719624665955830711633870545040915759347599025265181 (pp63) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 21.11 hours. Scaled time: 10.01 units (timescale=0.474). Factorization parameters were as follows: name: 62221_144 n: 8821066557700560914707538403741916445191036516315719696291370434325710113707949441060998120603176233357 m: 100000000000000000000000000000 deg: 5 c5: 28 c0: -55 skew: 1.14 type: snfs lss: 1 rlim: 1930000 alim: 1930000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1930000/1930000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [965000, 2565001) Primes: RFBsize:144125, AFBsize:144353, largePrimes:4136963 encountered Relations: rels:4269862, finalFF:339786 Max relations in full relation-set: 28 Initial matrix: 288544 x 339786 with sparse part having weight 35413273. Pruned matrix : 270492 x 271998 with weight 25939742. Total sieving time: 18.45 hours. Total relation processing time: 0.24 hours. Matrix solve time: 2.34 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000 total time: 21.11 hours. --------- CPU info (if available) ----------

(56·10¹⁴²-11)/9 = 6(2)₁₄₁1_<143> = 23911 · 42257 · C134
C134 = P55 · P80
P55 = 1143941411907996700520971946060340262736488878322319963_<55>
P80 = 53832597353146372166288374957906854282217567080482754146364408192442359473749921_<80>

Number: 62221_142 N=61581337422832947042565963830758116002701376652326624198705025783356556057053843625770686217875640758640672397218969955090412007972923 ( 134 digits) SNFS difficulty: 143 digits. Divisors found: r1=1143941411907996700520971946060340262736488878322319963 (pp55) r2=53832597353146372166288374957906854282217567080482754146364408192442359473749921 (pp80) Version: Msieve-1.40 Total time: 6.74 hours. Scaled time: 13.92 units (timescale=2.065). Factorization parameters were as follows: name: 62221_142 n: 61581337422832947042565963830758116002701376652326624198705025783356556057053843625770686217875640758640672397218969955090412007972923 m: 20000000000000000000000000000 deg: 5 c5: 175 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 1740000 alim: 1740000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1740000/1740000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [870000, 1670001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 274221 x 274469 Total sieving time: 6.37 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.25 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,143.000,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000 total time: 6.74 hours. --------- CPU info (if available) ----------

(56·10¹⁷⁴-11)/9 = 6(2)₁₇₃1_<175> = 659 · 8501 · 2621693 · 15087703 · 1862887311324908123884845247211972663_<37> · C119
C119 = P30 · P89
P30 = 452022591052245072685099765541_<30>
P89 = 33345589605560820714725890779712247472160401068383290810785202245000234921008604498692867_<89>

Run 8 out of 2318: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=432356704 Step 1 took 44297ms Step 2 took 20875ms ********** Factor found in step 2: 452022591052245072685099765541 Found probable prime factor of 30 digits: 452022591052245072685099765541 Probable prime cofactor 33345589605560820714725890779712247472160401068383290810 785202245000234921008604498692867 has 89 digits

May 22, 2009 (2nd)

By Dmitry Domanov / GMP-ECM 6.2.3, GGNFS/msieve / May 22, 2009
(16·10¹⁷⁶-7)/9 = 1(7)_176<177> = 3² · 59 · 615711081072019872468826193588606901197_<39> · C135
C135 = P43 · P93
P43 = 1772012938854214576783047007942566638416973_<43>
P93 = 306859161300820429718744093592872285344754892092073690101163543698285825481837814744085179507_<93>

N=543758404231006280078915314898360251643955593507494702574785941537600961230214196342616452411330988575208199411251642709824917020572311 ( 135 digits) SNFS difficulty: 177 digits. Divisors found: r1=1772012938854214576783047007942566638416973 (pp43) r2=306859161300820429718744093592872285344754892092073690101163543698285825481837814744085179507 (pp93) Version: Msieve v. 1.41 Total time: 83.47 hours. Scaled time: 165.45 units (timescale=1.982). Factorization parameters were as follows: n: 543758404231006280078915314898360251643955593507494702574785941537600961230214196342616452411330988575208199411251642709824917020572311 m: 200000000000000000000000000000000000 deg: 5 c5: 5 c0: -7 skew: 1.07 type: snfs lss: 1 rlim: 6300000 alim: 6300000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6300000/6300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3150000, 6350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1161103 x 1161351 Total sieving time: 81.17 hours. Total relation processing time: 0.25 hours. Matrix solve time: 1.94 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,177.000,5,0,0,0,0,0,0,0,0,6300000,6300000,28,28,53,53,2.5,2.5,100000 total time: 83.47 hours. --------- CPU info (if available) ----------

(7·10¹⁸⁸-43)/9 = (7)₁₈₇3_<188> = 19 · 227 · 30181 · 1971583899979817205738323467_<28> · C153
C153 = P49 · P104
P49 = 4805550249913806107164545818458971893599632427019_<49>
P104 = 63064369942282470443928890836206937269530197886183657029723257323673694166847341225815396360621173715417_<104>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3499185670 Step 1 took 524485ms Step 2 took 113000ms ********** Factor found in step 2: 4805550249913806107164545818458971893599632427019 Found probable prime factor of 49 digits: 4805550249913806107164545818458971893599632427019 Probable prime cofactor 63064369942282470443928890836206937269530197886183657029723257323673694166847341225815396360621173715417 has 104 digits

(73·10¹⁹²-1)/9 = 8(1)_192<193> = 73256271947274662782040893968743123700881_<41> · C153
C153 = P47 · P48 · P59
P47 = 12514183981701174831234244754445618634782464551_<47>
P48 = 267288759821310351191537888363735659318239313283_<48>
P59 = 33101853000094382825599338798034443619214831850089105550107_<59>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1770093265 Step 1 took 881297ms Step 2 took 194656ms ********** Factor found in step 2: 267288759821310351191537888363735659318239313283 Found probable prime factor of 48 digits: 267288759821310351191537888363735659318239313283 Composite cofactor 414242678578408103235078719600045420705685685982987391903794714703925355295201997258318971178094081756957 has 105 digits N=414242678578408103235078719600045420705685685982987391903794714703925355295201997258318971178094081756957 ( 105 digits) Divisors found: r1=12514183981701174831234244754445618634782464551 (pp47) r2=33101853000094382825599338798034443619214831850089105550107 (pp59) Version: Msieve v. 1.41 Total time: 8.29 hours. Scaled time: 16.43 units (timescale=1.982). Factorization parameters were as follows: n: 414242678578408103235078719600045420705685685982987391903794714703925355295201997258318971178094081756957 skew: 10245.06 # norm 9.53e+014 c5: 189000 c4: -4228453038 c3: -104481482087957 c2: 329571606307239790 c1: 3722167535783309214524 c0: 192804791565346169927120 # alpha -6.85 Y1: 26624677783 Y0: -73817495856612743163 # Murphy_E 1.91e-009 # M 380244343347328658347174459880259612066021441439257999459704883260043181974659152092827411667820947949767 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 256054 x 256302 Polynomial selection time: 0.74 hours. Total sieving time: 7.33 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 8.29 hours. --------- CPU info (if available) ----------

(73·10¹⁹⁰-1)/9 = 8(1)_190<191> = 3³ · 766373 · 576849289308102433339_<21> · 352770971508535022385843411436127_<33> · C131
C131 = P38 · P46 · P47
P38 = 53018587549308860488727446119008638117_<38>
P46 = 9830729640749698698057713596885562332720579109_<46>
P47 = 36957899619439052588389493711338143513746251349_<47>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1641020606 Step 1 took 111219ms Step 2 took 32437ms ********** Factor found in step 2: 53018587549308860488727446119008638117 Found probable prime factor of 38 digits: 53018587549308860488727446119008638117 Composite cofactor 363323119248671503681840442228888007882580930456529372102126201532931588055727988917152468041 has 93 digits N=363323119248671503681840442228888007882580930456529372102126201532931588055727988917152468041 ( 93 digits) Divisors found: r1=9830729640749698698057713596885562332720579109 (pp46) r2=36957899619439052588389493711338143513746251349 (pp47) Version: Msieve v. 1.41 Total time: 3.56 hours. Scaled time: 7.03 units (timescale=1.976). Factorization parameters were as follows: n: 363323119248671503681840442228888007882580930456529372102126201532931588055727988917152468041 m: 2201437169476072225733 deg: 4 c4: 15469200 c3: 64470243577 c2: -206162652068209327 c1: -157308994180603347 c0: 292072553235282416374746 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.372 # E(F1,F2) = 6.310444e-005 # GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1242934815. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 171992 x 172240 Polynomial selection time: 0.17 hours. Total sieving time: 3.23 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.10 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: gnfs,92,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 3.56 hours. --------- CPU info (if available) ----------

May 22, 2009

By Dmitry Domanov / GMP-ECM 6.2.3/GGNFS/Msieve / May 22, 2009
(73·10¹⁷³-1)/9 = 8(1)_173<174> = 7 · 4943 · 1059933049229_<13> · 64098166474883233335412841_<26> · C132
C132 = P37 · P45 · P51
P37 = 5651544344073065353949288742526199989_<37>
P45 = 460594228426107287120213438958014196056247359_<45>
P51 = 132550700853026894371155963466907255560307901107449_<51>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1247506212 Step 1 took 184500ms Step 2 took 57109ms ********** Factor found in step 2: 5651544344073065353949288742526199989 Found probable prime factor of 37 digits: 5651544344073065353949288742526199989 Composite cofactor 61052087786739683422486377745002538362377897736805318143684633775842372114767648010131181477191 has 95 digits N=61052087786739683422486377745002538362377897736805318143684633775842372114767648010131181477191 ( 95 digits) Divisors found: r1=460594228426107287120213438958014196056247359 (pp45) r2=132550700853026894371155963466907255560307901107449 (pp51) Version: Msieve v. 1.41 Total time: 4.57 hours. Scaled time: 8.99 units (timescale=1.969). Factorization parameters were as follows: n: 61052087786739683422486377745002538362377897736805318143684633775842372114767648010131181477191 m: 5723651533996740584386 deg: 4 c4: 56886312 c3: -96342723053 c2: -224961695606516291 c1: 242685027110432538 c0: 144224341387033435142535 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.139 # E(F1,F2) = 3.669255e-005 # GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1242912454. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1380001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 168434 x 168662 Polynomial selection time: 0.17 hours. Total sieving time: 4.19 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.07 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 4.57 hours. --------- CPU info (if available) ----------

May 21, 2009 (6th)

By Dmitry Domanov / GMP-ECM 6.2.3/GGNFS/Msieve / May 21, 2009
(16·10¹⁷⁴-7)/9 = 1(7)_174<175> = 2306250299_<10> · 74898255015998655946498827377_<29> · C137
C137 = P54 · P83
P54 = 478201468652324457339234840573843334174654778416210183_<54>
P83 = 21522287485721472882131698140452420826474012890115270934342109978718916791569225653_<83>

N=10291989484429551876179833835177150162938324601375571356928446368849810743540128602817703724734336895923865775996568943437420300203424499 ( 137 digits) SNFS difficulty: 175 digits. Divisors found: r1=478201468652324457339234840573843334174654778416210183 (pp54) r2=21522287485721472882131698140452420826474012890115270934342109978718916791569225653 (pp83) Version: Msieve v. 1.41 Total time: 84.67 hours. Scaled time: 168.32 units (timescale=1.988). Factorization parameters were as follows: n: 10291989484429551876179833835177150162938324601375571356928446368849810743540128602817703724734336895923865775996568943437420300203424499 m: 100000000000000000000000000000000000 deg: 5 c5: 8 c0: -35 skew: 1.34 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 6500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1127939 x 1128187 Total sieving time: 82.45 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.77 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,175.000,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,52,52,2.5,2.5,100000 total time: 84.67 hours. --------- CPU info (if available) ----------

(73·10¹⁸¹-1)/9 = 8(1)_181<182> = 3² · 71 · 401 · 7607 · 72912676783_<11> · 923219843886583_<15> · C147
C147 = P35 · P46 · P68
P35 = 20361161670231525367845505082480057_<35>
P46 = 1251616944363009719621705935812728955500311537_<46>
P68 = 24257137178864474300374832376502570787961784406903986047306381280607_<68>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=767694175 Step 1 took 135641ms Step 2 took 38156ms ********** Factor found in step 2: 20361161670231525367845505082480057 Found probable prime factor of 35 digits: 20361161670231525367845505082480057 Composite cofactor 30360643914804711280126537478375872549443004895718960937443150897826484577690408044401934796318699204093516462959 has 113 digits N=30360643914804711280126537478375872549443004895718960937443150897826484577690408044401934796318699204093516462959 ( 113 digits) Divisors found: r1=1251616944363009719621705935812728955500311537 (pp46) r2=24257137178864474300374832376502570787961784406903986047306381280607 (pp68) Version: Msieve v. 1.41 Total time: 17.82 hours. Scaled time: 35.43 units (timescale=1.988). Factorization parameters were as follows: name: 007 n: 30360643914804711280126537478375872549443004895718960937443150897826484577690408044401934796318699204093516462959 skew: 56060.73 # norm 4.56e+015 c5: 5400 c4: 925749786 c3: 139144709401328 c2: -2731545790006531265 c1: -191386617501901718109034 c0: -51794230834906778574463800 # alpha -6.75 Y1: 2605339957 Y0: -5623198788990427023859 # Murphy_E 7.80e-010 # M 26026941765268532581501352771223314519362970659436966324429862456488236216574342368172363669966953696988389310169 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 409831 x 410079 Total sieving time: 17.43 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.22 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 17.82 hours. --------- CPU info (if available) ----------

(16·10¹⁹⁹-7)/9 = 1(7)_199<200> = 264007 · 6353173 · C188
C188 = P41 · C147
P41 = 23291472982858333436228811919662999043691_<41>
C147 = [455066006465288415070009733577160112444400511082951782000226631417419627374631140800240793491446540584054470178200734178991550975951296244405242177_<147>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4270917581 Step 1 took 211781ms Step 2 took 52875ms ********** Factor found in step 2: 23291472982858333436228811919662999043691 Found probable prime factor of 41 digits: 23291472982858333436228811919662999043691 Composite cofactor 455066006465288415070009733577160112444400511082951782000226631417419627374631140800240793491446540584054470178200734178991550975951296244405242177 has 147 digits

May 21, 2009 (5th)

By matsui / Msieve / May 21, 2009
10¹⁷⁸-3 = (9)₁₇₇7_<178> = 13 · 887 · 10847 · C170
C170 = P41 · P48 · P82
P41 = 52170205801655912072668661692945628873867_<41>
P48 = 791376560196615965346312862807404223815327503783_<48>
P82 = 1936500685368344801593175804002836251063019833454008113128462336831727700966974861_<82>

N=79950905666669947318829189023504982624389597821120354119830593305197383715345289932645119668396902871410393219581156873135110146803694310686357178256548496856214460373321 ( 170 digits) SNFS difficulty: 179 digits. Divisors found: r1=52170205801655912072668661692945628873867 (pp41) r2=791376560196615965346312862807404223815327503783 (pp48) r3=1936500685368344801593175804002836251063019833454008113128462336831727700966974861 (pp82) Version: Msieve v. 1.41 Total time: 99.44 hours. Scaled time: 220.85 units (timescale=2.221). Factorization parameters were as follows: n: 79950905666669947318829189023504982624389597821120354119830593305197383715345289932645119668396902871410393219581156873135110146803694310686357178256548496856214460373321 m: 500000000000000000000000000000000000 deg: 5 c5: 8 c0: -75 skew: 1.56 type: snfs lss: 1 rlim: 6800000 alim: 6800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 200000 Factor base limits: 6800000/6800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3400000, 7800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1275737 x 1275985 Total sieving time: 96.45 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.61 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,179.000,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000 total time: 99.44 hours.

May 21, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / May 21, 2009
(56·10¹²⁶-11)/9 = 6(2)₁₂₅1_<127> = 1217 · 2621 · 196681 · 1314917 · C109
C109 = P50 · P59
P50 = 85460947370226636743108095203141443911505920048757_<50>
P59 = 88259094526073219007075664062010607115306266951250511756577_<59>

Number: 62221_126 N=7542705832236601216063235731698454018477684470697798773233660065331465340664513913820697047502655637555424789 ( 109 digits) SNFS difficulty: 128 digits. Divisors found: r1=85460947370226636743108095203141443911505920048757 (pp50) r2=88259094526073219007075664062010607115306266951250511756577 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.70 hours. Scaled time: 1.75 units (timescale=0.474). Factorization parameters were as follows: name: 62221_126 n: 7542705832236601216063235731698454018477684470697798773233660065331465340664513913820697047502655637555424789 m: 20000000000000000000000000 deg: 5 c5: 35 c0: -22 skew: 0.91 type: snfs lss: 1 rlim: 950000 alim: 950000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 950000/950000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [475000, 775001) Primes: RFBsize:74907, AFBsize:74524, largePrimes:2496810 encountered Relations: rels:2361847, finalFF:177094 Max relations in full relation-set: 28 Initial matrix: 149497 x 177094 with sparse part having weight 12725097. Pruned matrix : 138823 x 139634 with weight 7970789. Total sieving time: 3.31 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.26 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,950000,950000,26,26,47,47,2.3,2.3,50000 total time: 3.70 hours. --------- CPU info (if available) ----------

(17·10¹⁷⁹-11)/3 = 5(6)₁₇₈3_<180> = 31 · 10007 · 53192437 · 105051320748779_<15> · 374955728135539_<15> · 2878942959482939_<16> · C123
C123 = P51 · P72
P51 = 354049920548723132634303957269119976363078994390569_<51>
P72 = 855328836537558036336720562807522226820031225278213794850985182331674257_<72>

Number: 56663_179 N=302829106619154218377716355436978651473579332240491193108600419858021141565254322328800457872695512634703127245357140882233 ( 123 digits) Divisors found: r1=354049920548723132634303957269119976363078994390569 (pp51) r2=855328836537558036336720562807522226820031225278213794850985182331674257 (pp72) Version: Msieve-1.40 Total time: 75.65 hours. Scaled time: 151.75 units (timescale=2.006). Factorization parameters were as follows: name: 56663_179 # Murphy_E = 2.026034e-10, selected by Jeff Gilchrist n: 302829106619154218377716355436978651473579332240491193108600419858021141565254322328800457872695512634703127245357140882233 Y0: -433157679004605500978739 Y1: 18225977925839 c0: -18544938211182598116809527360 c1: -2140927006093851150814424 c2: -40473423879282093450 c3: 833121153677281 c4: -12735684640 c5: 19860 skew: 75263.93 type: gnfs # selected mechanically rlim: 6100000 alim: 6100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6100000/6100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3050000, 5750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 824469 x 824717 Total sieving time: 72.48 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.63 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6100000,6100000,27,27,52,52,2.5,2.5,100000 total time: 75.65 hours. --------- CPU info (if available) ----------

May 21, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 21, 2009
(56·10¹⁰⁵-11)/9 = 6(2)₁₀₄1_<106> = 19 · 275616891313033_<15> · C91
C91 = P35 · P56
P35 = 24330702448592325739955334584339839_<35>
P56 = 48835027773320238922833025911088665344601596148840538457_<56>

Number: 62221_105 N=1188190529821396970209289612592845440044925234583594455283508212115333084445779916636688423 ( 91 digits) SNFS difficulty: 107 digits. Divisors found: r1=24330702448592325739955334584339839 (pp35) r2=48835027773320238922833025911088665344601596148840538457 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.42 hours. Scaled time: 1.00 units (timescale=2.384). Factorization parameters were as follows: n: 1188190529821396970209289612592845440044925234583594455283508212115333084445779916636688423 m: 2000000000000000000000 deg: 5 c5: 7 c0: -44 skew: 1.44 type: snfs lss: 1 rlim: 240000 alim: 240000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 240000/240000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [120000, 240001) Primes: RFBsize:21221, AFBsize:21035, largePrimes:895240 encountered Relations: rels:798669, finalFF:63832 Max relations in full relation-set: 28 Initial matrix: 42322 x 63832 with sparse part having weight 3116321. Pruned matrix : 38783 x 39058 with weight 1292696. Total sieving time: 0.40 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,240000,240000,25,25,44,44,2.2,2.2,20000 total time: 0.42 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹²⁵-11)/9 = 6(2)₁₂₄1_<126> = 3 · C126
C126 = P52 · P74
P52 = 3806506880294352571346546015603433909291622425036793_<52>
P74 = 54487595564616145799918267616624286940343098904288600520561248151699639399_<74>

Number: 62221_125 N=207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407 ( 126 digits) SNFS difficulty: 127 digits. Divisors found: r1=3806506880294352571346546015603433909291622425036793 r2=54487595564616145799918267616624286940343098904288600520561248151699639399 Version: Total time: 1.09 hours. Scaled time: 2.60 units (timescale=2.378). Factorization parameters were as follows: n: 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407 m: 20000000000000000000000000 deg: 5 c5: 7 c0: -44 skew: 1.44 type: snfs lss: 1 rlim: 800000 alim: 800000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [400000, 720001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2509555 Max relations in full relation-set: Initial matrix: Pruned matrix : 117486 x 117729 Total sieving time: 0.96 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000 total time: 1.09 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 21, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 21, 2009
(56·10¹³⁷-11)/9 = 6(2)₁₃₆1_<138> = 3⁴ · 23789 · 31963 · 36405263 · 49736621128429_<14> · C106
C106 = P34 · P73
P34 = 1042522064367890213390144229142147_<34>
P73 = 5351937971935949863412995979448075596857523038286721401050467570506870027_<73>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2962973428 Step 1 took 7013ms Step 2 took 4220ms ********** Factor found in step 2: 1042522064367890213390144229142147 Found probable prime factor of 34 digits: 1042522064367890213390144229142147 Probable prime cofactor has 73 digits

(56·10¹⁹⁸-11)/9 = 6(2)₁₉₇1_<199> = 17 · 71 · 1877691063628923919_<19> · 39317325018936102524429_<23> · 100727673887609352544951_<24> · C132
C132 = P29 · P103
P29 = 71349951368303820813792160667_<29>
P103 = 9716003423286518136366458101254813472031564320708621201225088809711249287119537530935122345120997784109_<103>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3031718808 Step 1 took 8297ms Step 2 took 4920ms ********** Factor found in step 2: 71349951368303820813792160667 Found probable prime factor of 29 digits: 71349951368303820813792160667 Probable prime cofactor has 103 digits

(56·10¹⁸⁹-11)/9 = 6(2)₁₈₈1_<190> = 277 · 25277866982933_<14> · 40398247348837599795974405003_<29> · C146
C146 = P38 · C108
P38 = 54162299091422434499021060679582624167_<38>
C108 = [406130596790779999759153981712709459914372909456044656520865406171812435177580766081922259159004770290767081_<108>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=715898463 Step 1 took 9785ms Step 2 took 5252ms ********** Factor found in step 2: 54162299091422434499021060679582624167 Found probable prime factor of 38 digits: 54162299091422434499021060679582624167 Composite cofactor has 108 digits

(56·10¹⁸³-11)/9 = 6(2)₁₈₂1_<184> = 4093565809_<10> · 49145698624699_<14> · 485601426753367817_<18> · C143
C143 = P28 · P115
P28 = 9736459749091473825931494539_<28>
P115 = 6541497819942903558698373382749994533024229717901469902742645607369605026183770257812764739195205897479634921596237_<115>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2783513680 Step 1 took 9212ms Step 2 took 4944ms ********** Factor found in step 2: 9736459749091473825931494539 Found probable prime factor of 28 digits: 9736459749091473825931494539 Probable prime cofactor has 115 digits

(56·10¹⁵⁸-11)/9 = 6(2)₁₅₇1_<159> = 3 · 59 · C157
C157 = P30 · C128
P30 = 203211241393631956722915124219_<30>
C128 = [17299140354921275130942878961573349031729110752907845125819804596310155375128869475259027043222450254192642083192090196656125767_<128>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4165293997 Step 1 took 10729ms Step 2 took 5564ms ********** Factor found in step 2: 203211241393631956722915124219 Found probable prime factor of 30 digits: 203211241393631956722915124219 Composite cofactor has 128 digits

(56·10¹⁶⁹-11)/9 = 6(2)₁₆₈1_<170> = C170
C170 = P35 · P135
P35 = 90825936474910356580445455028314087_<35>
P135 = 685071078121065245380977100774338379718781727188337319868089778466636278967013267581132544372714137499174702411896983346835604803519083_<135>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=123382992 Step 1 took 3481ms Step 2 took 2488ms ********** Factor found in step 2: 90825936474910356580445455028314087 Found probable prime factor of 35 digits: 90825936474910356580445455028314087 Probable prime cofactor has 135 digits

(56·10¹³⁶-11)/9 = 6(2)₁₃₅1_<137> = C137
C137 = P50 · P88
P50 = 47116193896513763084644758936281326373029576202347_<50>
P88 = 1320612237034413540645554150519798422265330249675924859416078913978284141978929267347943_<88>

SNFS difficulty: 138 digits. Divisors found: r1=47116193896513763084644758936281326373029576202347 (pp50) r2=1320612237034413540645554150519798422265330249675924859416078913978284141978929267347943 (pp88) Version: Msieve v. 1.41 Total time: 2.29 hours. Scaled time: 6.24 units (timescale=2.723). Factorization parameters were as follows: n: 62222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 2000000000000000000000000000 deg: 5 c5: 35 c0: -22 skew: 0.91 type: snfs lss: 1 rlim: 1400000 alim: 1400000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [700000, 1300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 222824 x 223072 Total sieving time: 2.05 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.18 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,75000 total time: 2.29 hours.

May 21, 2009

By Robert Backstrom / GGNFS, Msieve / May 21, 2009
(52·10¹⁷⁰-7)/9 = 5(7)_170<171> = 20852144987_<11> · 79044397577_<11> · C150
C150 = P68 · P83
P68 = 22440932013872133921645504836737591772839461986141299394467185251929_<68>
P83 = 15620614489398361590137207913320714870296064367180578091040472815622493531339189187_<83>

Number: n N=350541147771494609491011242354777867405296059250495473592326054158821399535045616100799756842524277369580042636792251617397763429972324635079187691723 ( 150 digits) SNFS difficulty: 171 digits. Divisors found: Thu May 21 12:16:22 2009 prp68 factor: 22440932013872133921645504836737591772839461986141299394467185251929 Thu May 21 12:16:22 2009 prp83 factor: 15620614489398361590137207913320714870296064367180578091040472815622493531339189187 Thu May 21 12:16:22 2009 elapsed time 01:12:26 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 61.66 hours. Scaled time: 164.02 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_7_170 n: 350541147771494609491011242354777867405296059250495473592326054158821399535045616100799756842524277369580042636792251617397763429972324635079187691723 m: 10000000000000000000000000000000000 deg: 5 c5: 52 c0: -7 skew: 0.67 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2550000, 6067799) Primes: RFBsize:354971, AFBsize:354331, largePrimes:18240831 encountered Relations: rels:18861558, finalFF:753290 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2437626 hash collisions in 20937000 relations Msieve: matrix is 812926 x 813174 (214.4 MB) Total sieving time: 60.69 hours. Total relation processing time: 0.97 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,28,28,56,56,2.4,2.4,100000 total time: 61.66 hours. --------- CPU info (if available) ----------

(13·10¹⁷⁰+41)/9 = 1(4)₁₆₉9_<171> = 83 · 37643 · 1922390207061151_<16> · C149
C149 = P49 · P101
P49 = 1575121672855345298238023360609906942627058819383_<49>
P101 = 15268025271988546201862798038998621247627449241812295699219585367782233836956990474049954794008106537_<101>

Number: n N=24048997507612287288102100750520634911112589018110209838926532782366722172082602334303006601667608485021999452619553254832970652887124101622504606671 ( 149 digits) SNFS difficulty: 171 digits. Divisors found: Thu May 21 14:11:46 2009 prp49 factor: 1575121672855345298238023360609906942627058819383 Thu May 21 14:11:46 2009 prp101 factor: 15268025271988546201862798038998621247627449241812295699219585367782233836956990474049954794008106537 Thu May 21 14:11:46 2009 elapsed time 01:23:14 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 41.94 hours. Scaled time: 111.09 units (timescale=2.649). Factorization parameters were as follows: name: KA_1_4_169_9 n: 24048997507612287288102100750520634911112589018110209838926532782366722172082602334303006601667608485021999452619553254832970652887124101622504606671 m: 10000000000000000000000000000000000 deg: 5 c5: 13 c0: 41 skew: 1.26 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 4812883) Primes: RFBsize:348513, AFBsize:347692, largePrimes:16399716 encountered Relations: rels:15549600, finalFF:675814 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1579804 hash collisions in 16873984 relations Msieve: matrix is 902266 x 902514 (242.4 MB) Total sieving time: 41.36 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 41.94 hours. --------- CPU info (if available) ----------

May 20, 2009 (3rd)

By Dmitry Domanov / GMP-ECM 6.2.3, GGNFS/Msieve / May 20, 2009
(73·10¹⁷³-1)/9 = 8(1)_173<174> = 7 · 4943 · 1059933049229_<13> · C158
C158 = P26 · C132
P26 = 64098166474883233335412841_<26>
C132 = [345038581425000928450184633893862071554589588600861750152497688160450839810744310320911058217737288283002897503366245665576907950899_<132>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=460137404 Step 1 took 41172ms Step 2 took 11828ms ********** Factor found in step 2: 64098166474883233335412841 Found probable prime factor of 26 digits: 64098166474883233335412841 Composite cofactor 345038581425000928450184633893862071554589588600861750152497688160450839810744310320911058217737288283002897503366245665576907950899 has 132 digits

(16·10¹⁷¹-7)/9 = 1(7)_171<172> = 2159081 · 6112989193_<10> · 1204075884061927058546730881_<28> · C129
C129 = P56 · P73
P56 = 28439831557188093353879668494862682918380292611871233807_<56>
P73 = 3933453600796913095720722985325855260149941585902703532789048980867241007_<73>

N=111866757844679185887968729281774448067931340871359537390276493296195096332957079943344641551979112580133063024428735821115123649 ( 129 digits) SNFS difficulty: 172 digits. Divisors found: r1=28439831557188093353879668494862682918380292611871233807 (pp56) r2=3933453600796913095720722985325855260149941585902703532789048980867241007 (pp73) Version: Msieve v. 1.41 Total time: 55.00 hours. Scaled time: 109.34 units (timescale=1.988). Factorization parameters were as follows: n: 111866757844679185887968729281774448067931340871359537390276493296195096332957079943344641551979112580133063024428735821115123649 m: 20000000000000000000000000000000000 deg: 5 c5: 5 c0: -7 skew: 1.07 type: snfs lss: 1 rlim: 5200000 alim: 5200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2600000, 5000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 961428 x 961676 Total sieving time: 53.49 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.27 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000 total time: 55.00 hours. --------- CPU info (if available) ----------

(73·10¹⁹⁰-1)/9 = 8(1)_190<191> = 3³ · 766373 · 576849289308102433339_<21> · C163
C163 = P33 · C131
P33 = 352770971508535022385843411436127_<33>
C131 = [19262878606573673376074258194783601287435893348319362805902003690630345538687715610774754588966646448026626420304138049204776918797_<131>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3579367891 Step 1 took 40735ms Step 2 took 12609ms ********** Factor found in step 2: 352770971508535022385843411436127 Found probable prime factor of 33 digits: 352770971508535022385843411436127 Composite cofactor 19262878606573673376074258194783601287435893348319362805902003690630345538687715610774754588966646448026626420304138049204776918797 has 131 digits

(73·10¹⁷⁹-1)/9 = 8(1)_179<180> = 7 · 29 · 67 · 21269 · C172
C172 = P41 · P131
P41 = 47141841003406331455972300887242733651907_<41>
P131 = 59477937477999248614204295322005295328835826506670111421059365117724762292797146126309564949352193967528628063664436708337272494617_<131>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2284984890 Step 1 took 165109ms ********** Factor found in step 1: 47141841003406331455972300887242733651907 Found probable prime factor of 41 digits: 47141841003406331455972300887242733651907 Probable prime cofactor 59477937477999248614204295322005295328835826506670111421059365117724762292797146126309564949352193967528628063664436708337272494617 has 131 digits

May 20, 2009 (2nd)

By Robert Backstrom / GGNFS / May 20, 2009
4·10¹⁷⁰+7 = 4(0)₁₆₉7_<171> = 11 · 23 · 37 · 2381 · 2531 · 23039 · 1367480531_<10> · C147
C147 = P47 · P101
P47 = 22070578087533539660066827927884256765089556891_<47>
P101 = 10197359262644066179879009668764560198414918046657958570180948390548824665266349600950111435706326543_<101>

Number: n N=225061613892819300304785905266740211732831812868396480313631702593877904934930918137401620751717308464609538424488999385361130786232218389221857813 ( 147 digits) SNFS difficulty: 170 digits. Divisors found: r1=22070578087533539660066827927884256765089556891 (pp47) r2=10197359262644066179879009668764560198414918046657958570180948390548824665266349600950111435706326543 (pp101) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 37.67 hours. Scaled time: 98.95 units (timescale=2.627). Factorization parameters were as follows: name: KA_4_0_169_7 n: 225061613892819300304785905266740211732831812868396480313631702593877904934930918137401620751717308464609538424488999385361130786232218389221857813 m: 10000000000000000000000000000000000 deg: 5 c5: 4 c0: 7 skew: 1.12 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [2450000, 4250001) Primes: RFBsize:341992, AFBsize:341158, largePrimes:16380774 encountered Relations: rels:16086164, finalFF:804371 Max relations in full relation-set: 28 Initial matrix: 683214 x 804371 with sparse part having weight 83408290. Pruned matrix : 597975 x 601455 with weight 63746608. Total sieving time: 33.20 hours. Total relation processing time: 0.48 hours. Matrix solve time: 3.16 hours. Total square root time: 0.82 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000 total time: 37.67 hours. --------- CPU info (if available) ----------

May 20, 2009

Factorizations of 622...221 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 19, 2009 (4th)

By Dmitry Domanov / GGNFS/Msieve, GMP-ECM 6.2.3 / May 19, 2009
(7·10¹⁸⁰-43)/9 = (7)₁₇₉3_<180> = 53 · 197 · 422057 · 741131 · 1131199217758037948475947876693_<31> · C135
C135 = P64 · P71
P64 = 2741369082874657399663051277237026829017586667572935865244850717_<64>
P71 = 76796378648023087638003648915673883503681198485916992643055270266992439_<71>

Number: 777 N=210527218102425973724818558615766578439790005099467290507542270053221747074507541204557915603489023170770125680574714982426615122728763 ( 135 digits) SNFS difficulty: 180 digits. Divisors found: r1=2741369082874657399663051277237026829017586667572935865244850717 (pp64) r2=76796378648023087638003648915673883503681198485916992643055270266992439 (pp71) Version: Msieve v. 1.41 Total time: 158.15 hours. Scaled time: 313.46 units (timescale=1.982). Factorization parameters were as follows: n: 210527218102425973724818558615766578439790005099467290507542270053221747074507541204557915603489023170770125680574714982426615122728763 m: 1000000000000000000000000000000000000 deg: 5 c5: 7 c0: -43 skew: 1.44 type: snfs lss: 1 rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3600000, 5900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1283421 x 1283669 Total sieving time: 155.28 hours. Total relation processing time: 0.27 hours. Matrix solve time: 2.33 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,180.000,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000 total time: 158.15 hours. --------- CPU info (if available) ----------

(7·10²⁰⁰-43)/9 = (7)₁₉₉3_<200> = 991073183 · C191
C191 = P40 · C152
P40 = 3937154377208831195317050869489643571199_<40>
C152 = [19932756512603613805537617547909718330804698132888310510455011242343011729605214247504057026096081092532311130097139778827231495420334733940846765405069_<152>]

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1296127361 Step 1 took 829141ms Step 2 took 159953ms ********** Factor found in step 2: 3937154377208831195317050869489643571199 Found probable prime factor of 40 digits: 3937154377208831195317050869489643571199 Composite cofactor 19932756512603613805537617547909718330804698132888310510455011242343011729605214247504057026096081092532311130097139778827231495420334733940846765405069 has 152 digits

May 19, 2009 (3rd)

By matsui / Msieve / May 19, 2009
8·10¹⁸⁰-9 = 7(9)₁₇₉1_<181> = 826115977894170609050375729157582021497_<39> · C142
C142 = P67 · P75
P67 = 9990207070327391855783197701498143287718371662893791939986474480751_<67>
P75 = 969336296313865853470535064289775123620533028668230038800912477861614266753_<75>

N=9683870320959750397301131599191235511655411576027658067144718311274518875633720728729028560156827649352670707054841461900759820696819277771503 ( 142 digits) SNFS difficulty: 180 digits. Divisors found: r1=9990207070327391855783197701498143287718371662893791939986474480751 (pp67) r2=969336296313865853470535064289775123620533028668230038800912477861614266753 (pp75) Version: Msieve v. 1.41 Total time: 110.65 hours. Scaled time: 244.98 units (timescale=2.214). Factorization parameters were as follows: n: 9683870320959750397301131599191235511655411576027658067144718311274518875633720728729028560156827649352670707054841461900759820696819277771503 m: 1000000000000000000000000000000000000 deg: 5 c5: 8 c0: -9 skew: 1.02 type: snfs lss: 1 rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 200000 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3600000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1294696 x 1294944 Total sieving time: 106.54 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.78 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,180.000,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000 total time: 110.65 hours.

May 19, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / May 19, 2009
(82·10¹⁹⁸-1)/9 = 9(1)_198<199> = 3² · 347 · C196
C196 = P87 · P109
P87 = 436939136360240984927360625309074935876631115857657607436178934760710293610292472591579_<87>
P109 = 6676954438986529421607213490324435297594479058174569446376089299972729546356176059887751621704278177785185383_<109>

Number: n N=2917422706087451524531255559113388123954886683032696481303589853061514925107624435194079766606183513003878037499555270928950083609065357384281495712811755078805991390045184473618671505318959689757 ( 196 digits) SNFS difficulty: 201 digits. Divisors found: Tue May 19 05:13:09 2009 prp87 factor: 436939136360240984927360625309074935876631115857657607436178934760710293610292472591579 Tue May 19 05:13:09 2009 prp109 factor: 6676954438986529421607213490324435297594479058174569446376089299972729546356176059887751621704278177785185383 Tue May 19 05:13:09 2009 elapsed time 13:39:46 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20050930-k8 Total time: 40.20 hours. Scaled time: 81.00 units (timescale=2.015). Factorization parameters were as follows: name: KA_9_1_198 n: 2917422706087451524531255559113388123954886683032696481303589853061514925107624435194079766606183513003878037499555270928950083609065357384281495712811755078805991390045184473618671505318959689757 m: 10000000000000000000000000000000000000000 deg: 5 c5: 41 c0: -50 skew: 1.04 type: snfs lss: 1 rlim: 16000000 alim: 16000000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved special-q in [8000000, 17000141) Primes: RFBsize:1031130, AFBsize:1031439, largePrimes:36170229 encountered Relations: rels:35462145, finalFF:1658980 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 4758809 hash collisions in 38486645 relations Msieve: matrix is 2854694 x 2854942 (777.1 MB) Total sieving time: 39.37 hours. Total relation processing time: 0.82 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,56,56,2.6,2.6,100000 total time: 40.20 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.70 BogoMIPS).

(55·10¹⁶⁶+71)/9 = 6(1)₁₆₅9_<167> = 3² · 285643157 · C158
C158 = P46 · P112
P46 = 4368395824318766408050439945935647525108707809_<46>
P112 = 5441665761123586513039701393455608632083915097455189199613841488885076266307031749893027851414099021773762658907_<112>

Number: n N=23771349988230677119949782157008310396142707023750348259839893370139875105742944357634737445469850540792487658964375109431112528945069238224822787510794304763 ( 158 digits) SNFS difficulty: 167 digits. Divisors found: Tue May 19 17:51:37 2009 prp46 factor: 4368395824318766408050439945935647525108707809 Tue May 19 17:51:37 2009 prp112 factor: 5441665761123586513039701393455608632083915097455189199613841488885076266307031749893027851414099021773762658907 Tue May 19 17:51:37 2009 elapsed time 00:59:13 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 46.95 hours. Scaled time: 124.89 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_1_165_9 n: 23771349988230677119949782157008310396142707023750348259839893370139875105742944357634737445469850540792487658964375109431112528945069238224822787510794304763 m: 1000000000000000000000000000000000 deg: 5 c5: 550 c0: 71 skew: 0.66 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2200000, 4930207) Primes: RFBsize:309335, AFBsize:308675, largePrimes:16930723 encountered Relations: rels:17097659, finalFF:662576 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2077248 hash collisions in 18962584 relations Msieve: matrix is 711056 x 711304 (188.0 MB) Total sieving time: 46.23 hours. Total relation processing time: 0.73 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,56,56,2.4,2.4,100000 total time: 46.95 hours. --------- CPU info (if available) ----------

May 19, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 19, 2009
2·10¹⁸¹-1 = 1(9)_181<182> = 19 · 71 · 7349 · 808897818779368181_<18> · 797129087967153857493783971_<27> · C130
C130 = P46 · P84
P46 = 5050517525163785428349019657192204840675990331_<46>
P84 = 619486140631122497714177220241924734371086778583423922913708782283498388270677109979_<84>

Number: 19999_181 N=3128725609853561538026773920634567520995491992088880828324972714133336327873248318256123375586149260625874239143237635528827613049 ( 130 digits) SNFS difficulty: 181 digits. Divisors found: r1=5050517525163785428349019657192204840675990331 r2=619486140631122497714177220241924734371086778583423922913708782283498388270677109979 Version: Total time: 68.24 hours. Scaled time: 162.76 units (timescale=2.385). Factorization parameters were as follows: n: 3128725609853561538026773920634567520995491992088880828324972714133336327873248318256123375586149260625874239143237635528827613049 m: 1000000000000000000000000000000000000 deg: 5 c5: 20 c0: -1 skew: 0.55 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [2900000, 4800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 17839570 Max relations in full relation-set: Initial matrix: Pruned matrix : 1166869 x 1167117 Total sieving time: 62.68 hours. Total relation processing time: 1.76 hours. Matrix solve time: 3.07 hours. Time per square root: 0.73 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,53,53,2.5,2.5,100000 total time: 68.24 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 18, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 18, 2009
(55·10¹⁶⁷+53)/9 = 6(1)₁₆₆7_<168> = 13 · C167
C167 = P51 · P117
P51 = 413253709863765149819165994687158966560294819480339_<51>
P117 = 113752268610108864645974297516771880453518903037560549478996788182332828844323184288710023807427966999107247784733531_<117>

Number: n N=47008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547009 ( 167 digits) SNFS difficulty: 170 digits. Divisors found: Mon May 18 20:45:42 2009 prp51 factor: 413253709863765149819165994687158966560294819480339 Mon May 18 20:45:42 2009 prp117 factor: 113752268610108864645974297516771880453518903037560549478996788182332828844323184288710023807427966999107247784733531 Mon May 18 20:45:42 2009 elapsed time 01:47:01 (Msieve 1.39 - dependency 5) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 46.69 hours. Scaled time: 123.67 units (timescale=2.649). Factorization parameters were as follows: name: KA_6_1_166_7 n: 47008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547009 m: 5000000000000000000000000000000000 deg: 5 c5: 44 c0: 1325 skew: 1.98 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2400000, 5036893) Primes: RFBsize:335439, AFBsize:335533, largePrimes:16351362 encountered Relations: rels:15644308, finalFF:647400 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1750957 hash collisions in 17268406 relations Msieve: matrix is 861002 x 861250 (230.9 MB) Total sieving time: 46.06 hours. Total relation processing time: 0.63 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000 total time: 46.69 hours. --------- CPU info (if available) ----------

May 18, 2009 (3rd)

By Dmitry Domanov / GMP-ECM 6.2.3, GGNFS, Msieve 1.41 / May 18, 2009
2·10²³²-1 = 1(9)_232<233> = 7 · 173137 · 42049591 · C219
C219 = P38 · P182
P38 = 34613759961280378907193267864768175303_<38>
P182 = 11337871068816284810015281720676567521820709766247790016536458359116649482490012289408508986811315047442941807203647099955100565546682002698657209705791404051679009408588287240060857_<182>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1689352593 Step 1 took 410609ms Step 2 took 104703ms ********** Factor found in step 2: 34613759961280378907193267864768175303 Found probable prime factor of 38 digits: 34613759961280378907193267864768175303 Probable prime cofactor 11337871068816284810015281720676567521820709766247790016536458359116649482490012289408508986811315047442941807203647099955100565546682002698657209705791404051679009408588287240060857 has 182 digits

(7·10¹⁷⁹-43)/9 = (7)₁₇₈3_<179> = 29 · 74139184723_<11> · 5678444893385647_<16> · 64191352839380917_<17> · C134
C134 = P53 · P82
P53 = 59768195256934827918992906434416007822747135583378717_<53>
P82 = 1660479967082549350076027500591027695979166379603958880084664687018341548117976293_<82>

Number: 2 N=99243890892818525257757099486749168779709129287517878619947908485429606390314043914415323816305774703347821779218335872529329446756081 ( 134 digits) SNFS difficulty: 180 digits. Divisors found: r1=59768195256934827918992906434416007822747135583378717 (pp53) r2=1660479967082549350076027500591027695979166379603958880084664687018341548117976293 (pp82) Version: Msieve v. 1.41 Total time: 142.93 hours. Scaled time: 284.15 units (timescale=1.988). Factorization parameters were as follows: n: 99243890892818525257757099486749168779709129287517878619947908485429606390314043914415323816305774703347821779218335872529329446756081 m: 500000000000000000000000000000000000 deg: 5 c5: 112 c0: -215 skew: 1.14 type: snfs lss: 1 rlim: 7100000 alim: 7100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7100000/7100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3550000, 5650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1233288 x 1233536 Total sieving time: 140.43 hours. Total relation processing time: 0.27 hours. Matrix solve time: 2.09 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,180.000,5,0,0,0,0,0,0,0,0,7100000,7100000,28,28,53,53,2.5,2.5,100000 total time: 142.93 hours. --------- CPU info (if available) ----------

May 18, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3 / May 18, 2009
2·10²⁴⁵-1 = 1(9)_245<246> = 240139 · C240
C240 = P35 · P206
P35 = 11646344158366741257794536820925991_<35>
P206 = 71511794816116647592466076649315262164366978239860741017711346458660357589133354997489778453665412237637499789509689866120922247059753039227205632490112635124358150084519402014002012700683540453240769740251_<206>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4173179287 Step 1 took 6145ms Step 2 took 3728ms ********** Factor found in step 2: 11646344158366741257794536820925991 Found probable prime factor of 35 digits: 11646344158366741257794536820925991 Probable prime cofactor has 206 digits

May 18, 2009

By Erik Branger / GGNFS, Msieve / May 18, 2009
(53·10¹⁷⁹-17)/9 = 5(8)₁₇₈7_<180> = 13 · 8609 · 2466439 · 1905016558247958781387_<22> · 8442905563306619451552613_<25> · C123
C123 = P49 · P75
P49 = 1267882575806183686123062369811279771630970712791_<49>
P75 = 104615780893553633888163173944050869226186736163185458497293997297646226469_<75>

Number: 58887_179 N=132640525749294118102139295123428335192313886562409838069300157486717226157984219970666790975658435729365925900696341064979 ( 123 digits) Divisors found: r1=1267882575806183686123062369811279771630970712791 (pp49) r2=104615780893553633888163173944050869226186736163185458497293997297646226469 (pp75) Version: Msieve v. 1.41 Total time: 103.57 hours. Scaled time: 81.20 units (timescale=0.784). Factorization parameters were as follows: # Murphy_E = 2.204181e-10, selected by Jeff Gilchrist n: 132640525749294118102139295123428335192313886562409838069300157486717226157984219970666790975658435729365925900696341064979 Y0: -360317732448563326023454 Y1: 19879181277307 c0: 171606085697399885470075292375 c1: -919211884570549739620675 c2: 6162561620072014696 c3: -1776083482988118 c4: -4172818468 c5: 21840 skew: 146902.99 type: gnfs # selected mechanically rlim: 6000000 alim: 6000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3000000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 812357 x 812605 Total sieving time: 97.10 hours. Total relation processing time: 0.27 hours. Matrix solve time: 4.27 hours. Time per square root: 1.93 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,52,52,2.5,2.5,100000 total time: 103.57 hours. --------- CPU info (if available) ----------

May 17, 2009 (7th)

By Dmitry Domanov / Msieve v. 1.41, GMP-ECM 6.2.3 / May 17, 2009
2·10¹⁷⁷-3 = 1(9)₁₇₆7_<178> = 17 · 66090659226826860491_<20> · 314129679887073807583524645188651_<33> · C124
C124 = P57 · P68
P57 = 129436443535881527128893364288064480493161761142268211249_<57>
P68 = 43779968748061432046513482796553162771143586000974553425324771322949_<68>

Number: 1 N=5666723452861111419953301719983874645151689206796263127100108210064996380732130563446722510620008860655369666194925533653301 ( 124 digits) Divisors found: r1=129436443535881527128893364288064480493161761142268211249 (pp57) r2=43779968748061432046513482796553162771143586000974553425324771322949 (pp68) Version: Msieve v. 1.41 Total time: 64.89 hours. Scaled time: 129.00 units (timescale=1.988). Factorization parameters were as follows: n: 5666723452861111419953301719983874645151689206796263127100108210064996380732130563446722510620008860655369666194925533653301 Y0: -790479467134143134043274 Y1: 32457700167143 c0: -16608921037930062398718064421235 c1: 204502172404307051875471623 c2: -475301048895667076195 c3: -3826111044588199 c4: 6563015646 c5: 18360 skew: 335696.21 type: gnfs # selected mechanically rlim: 6600000 alim: 6600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6600000/6600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3300000, 6200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 853192 x 853440 Total sieving time: 63.48 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.94 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6600000,6600000,27,27,52,52,2.5,2.5,100000 total time: 64.89 hours. --------- CPU info (if available) ----------

(8·10¹⁷³-17)/9 = (8)₁₇₂7_<173> = 3 · 19 · 238591 · 266183 · 6010441682603_<13> · 812262305277809501754934760781703_<33> · C115
C115 = P49 · P67
P49 = 2611259137894710237293454858163599958892111103623_<49>
P67 = 1926129971804758511475517763482213919232130440459976838959776938821_<67>

N=5029624489648056247300436114909387948363823244892596172024214674079949553164223403365426542863909717715506862448483 ( 115 digits) Divisors found: r1=2611259137894710237293454858163599958892111103623 (pp49) r2=1926129971804758511475517763482213919232130440459976838959776938821 (pp67) Version: Msieve v. 1.41 Total time: 22.88 hours. Scaled time: 45.48 units (timescale=1.988). Factorization parameters were as follows: name: 0 n: 5029624489648056247300436114909387948363823244892596172024214674079949553164223403365426542863909717715506862448483 skew: 36469.77 # norm 1.93e+016 c5: 170100 c4: -10736202576 c3: -1186048453213825 c2: 14042271287297154850 c1: 548613656918148741678540 c0: 1532467212163374559964486256 # alpha -7.17 Y1: 2806801040923 Y0: -7837331434948602045395 # Murphy_E 5.77e-010 # M 4373931990339949704516262703984833457081464005125254720617819565817044248881822484578247306882686022685927858970917 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 453024 x 453272 Total sieving time: 22.44 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.26 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 22.88 hours. --------- CPU info (if available) ----------

2·10²⁰⁶-1 = 1(9)_206<207> = 11887 · C203
C203 = P32 · C171
P32 = 25251681423007905250365508795903_<32>
C171 = [666296345653486704742396440597318758413330523030411841134328740685319859888372657484412271028953068923412326473632165793283237236740121087632239829994708821140851105993359_<171>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1034025118 Step 1 took 365484ms Step 2 took 91844ms ********** Factor found in step 2: 25251681423007905250365508795903 Found probable prime factor of 32 digits: 25251681423007905250365508795903 Composite cofactor 666296345653486704742396440597318758413330523030411841134328740685319859888372657484412271028953068923412326473632165793283237236740121087632239829994708821140851105993359 has 171 digits

May 17, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / May 17, 2009
(55·10¹⁵⁶+71)/9 = 6(1)₁₅₅9_<157> = 7 · 19 · 89 · 18371 · 171079 · C144
C144 = P55 · P89
P55 = 4370158092582282757313947484456642816270989901770322191_<55>
P89 = 37588230741138358916968159138254050527582219668790482732985280376540552048714496247601473_<89>

Number: n N=164266510759235935151091684199368678071275955875794973838775544060115590128095146270263568553806905435199397302142613446385652138637818176187343 ( 144 digits) SNFS difficulty: 157 digits. Divisors found: Sun May 17 13:36:38 2009 prp55 factor: 4370158092582282757313947484456642816270989901770322191 Sun May 17 13:36:38 2009 prp89 factor: 37588230741138358916968159138254050527582219668790482732985280376540552048714496247601473 Sun May 17 13:36:38 2009 elapsed time 00:38:11 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 18.14 hours. Scaled time: 48.25 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_1_155_9 n: 164266510759235935151091684199368678071275955875794973838775544060115590128095146270263568553806905435199397302142613446385652138637818176187343 m: 10000000000000000000000000000000 deg: 5 c5: 550 c0: 71 skew: 0.66 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1500000, 2621263) Primes: RFBsize:216816, AFBsize:216593, largePrimes:12448399 encountered Relations: rels:11358348, finalFF:405451 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 973747 hash collisions in 12361528 relations Msieve: matrix is 559501 x 559749 (151.1 MB) Total sieving time: 17.86 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000 total time: 18.14 hours. --------- CPU info (if available) ----------

(55·10¹⁵⁷+71)/9 = 6(1)₁₅₆9_<158> = 3² · 1471403 · 802664521 · C142
C142 = P58 · P85
P58 = 1686182319884758962774964750881255991601351889743917277737_<58>
P85 = 3409631426198123185000501403935973337864779640058934109973986572635032460917715202261_<85>

Number: n N=5749260228178730669619786717761222950011415158355549533147526451268751883270957466810123899031638901689018728723513873259203959052863467363357 ( 142 digits) SNFS difficulty: 159 digits. Divisors found: Sun May 17 18:57:23 2009 prp58 factor: 1686182319884758962774964750881255991601351889743917277737 Sun May 17 18:57:23 2009 prp85 factor: 3409631426198123185000501403935973337864779640058934109973986572635032460917715202261 Sun May 17 18:57:23 2009 elapsed time 00:42:44 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 23.25 hours. Scaled time: 61.08 units (timescale=2.627). Factorization parameters were as follows: name: KA_6_1_156_9 n: 5749260228178730669619786717761222950011415158355549533147526451268751883270957466810123899031638901689018728723513873259203959052863467363357 m: 20000000000000000000000000000000 deg: 5 c5: 1375 c0: 568 skew: 0.84 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1600000, 3000103) Primes: RFBsize:230209, AFBsize:230864, largePrimes:13258094 encountered Relations: rels:12352354, finalFF:499172 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1168747 hash collisions in 13306719 relations Msieve: matrix is 600048 x 600296 (161.2 MB) Total sieving time: 22.97 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,56,56,2.4,2.4,100000 total time: 23.25 hours. --------- CPU info (if available) ----------

May 17, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.3 / May 17, 2009
2·10²⁴⁷-1 = 1(9)_247<248> = 5711 · 5137651 · C237
C237 = P33 · P205
P33 = 109424217918630909136935706451429_<33>
P205 = 6229307717727602487152483306982713621811871446270813768407187294030930000936284989180582851699942671495245102701667423676129508232560794431964653471639690945651238874214201094168491986383412060065017416271_<205>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1912754877 Step 1 took 18573ms Step 2 took 14897ms ********** Factor found in step 2: 109424217918630909136935706451429 Found probable prime factor of 33 digits: 109424217918630909136935706451429 Probable prime cofactor has 205 digits Done!

2·10²⁴⁰-1 = 1(9)_240<241> = 30977 · C236
C236 = P29 · C208
P29 = 12900409695855239366375680297_<29>
C208 = [5004804723284328509504727413794179674007575588977579484001085955783285781518184216385475235750566319669217329827167346224955993379403688987397077202076056166105889455325049497934984058409692206566091055812071_<208>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3362628703 Step 1 took 18557ms Step 2 took 14457ms ********** Factor found in step 2: 12900409695855239366375680297 Found probable prime factor of 29 digits: 12900409695855239366375680297 Composite cofactor has 208 digits

2·10²⁰⁵-1 = 1(9)_205<206> = 4871 · 2292880818603421_<16> · C187
C187 = P31 · C157
P31 = 1129082288029883803778855245661_<31>
C157 = [1586005869640370385835630004795171489748136970111735468000037034576203712150943132322655517008937091427800298435286635359428161072876813941823046361696157249_<157>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3975420477 Step 1 took 12357ms Step 2 took 11288ms ********** Factor found in step 2: 1129082288029883803778855245661 Found probable prime factor of 31 digits: 1129082288029883803778855245661 Composite cofactor has 157 digits

May 17, 2009 (4th)

By matsui / Msieve / May 17, 2009
7·10¹⁷⁰-3 = 6(9)₁₆₉7_<171> = 1429327603703_<13> · 28390070271134877038117841913_<29> · C131
C131 = P53 · P79
P53 = 10977412137489495157200178568512469140915422117788701_<53>
P79 = 1571447302297785507555396244163363334714959786940690062024588758974391266160223_<79>

N=17250424689668834463131362979763025513450745051057365655701643284974919725337463089471895545976264413296899763464783165863925040323 ( 131 digits) SNFS difficulty: 170 digits. Divisors found: r1=10977412137489495157200178568512469140915422117788701 (pp53) r2=1571447302297785507555396244163363334714959786940690062024588758974391266160223 (pp79) Version: Msieve v. 1.41 Total time: 43.50 hours. Scaled time: 95.83 units (timescale=2.203). Factorization parameters were as follows: n: 17250424689668834463131362979763025513450745051057365655701643284974919725337463089471895545976264413296899763464783165863925040323 m: 10000000000000000000000000000000000 deg: 5 c5: 7 c0: -3 skew: 0.84 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 4550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 925874 x 926122 Total sieving time: 41.19 hours. Total relation processing time: 0.10 hours. Matrix solve time: 2.10 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 43.50 hours.

May 17, 2009 (3rd)

By Markus Tervooren / ggnfs/msieve / May 17, 2009
(55·10¹⁶⁰+71)/9 = 6(1)₁₅₉9_<161> = 3 · 149 · 21107 · 1084075229719_<13> · C142
C142 = P38 · P104
P38 = 88539989319060976418882479999944058891_<38>
P104 = 67481893525870289348177804373535358169251913889732089510397032622620280152860264580806539879951990357159_<104>

Msieve v. 1.41 Sat May 16 23:48:25 2009 random seeds: 1adbc9bd 4cfcd870 factoring 5974846132010565473273718653317702536894929614781964497842106328436804159921963100290714032559044192138130940159247390971510433112663219450669 (142 digits) searching for 15-digit factors commencing number field sieve (142-digit input) R0: -100000000000000000000000000000000 R1: 1 A0: 71 A1: 0 A2: 0 A3: 0 A4: 0 A5: 55 skew 1.05, size 1.984130e-11, alpha 1.074395, combined = 4.937228e-10 commencing square root phase reading relations for dependency 1 read 278577 cycles cycles contain 1059584 unique relations read 1059584 relations multiplying 848856 relations multiply complete, coefficients have about 23.21 million bits initial square root is modulo 4621231 sqrtTime: 135 prp38 factor: 88539989319060976418882479999944058891 prp104 factor: 67481893525870289348177804373535358169251913889732089510397032622620280152860264580806539879951990357159 elapsed time 00:02:16 Total sieving time: 18:12:01

May 17, 2009 (2nd)

Factorizations of 199...99 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 17, 2009

By Serge Batalov / PFGW / Mar 16, 2009
(16·10⁵⁶⁰⁸²-61)/9 = 1(7)₅₆₀₈₁1_<56083> is PRP.

May 16, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / May 16, 2009
(55·10¹⁷³+53)/9 = 6(1)₁₇₂7_<174> = 13 · 29 · 107 · C170
C170 = P77 · P94
P77 = 12576082971806871968069729416319272329315487489596105277919238868516031336329_<77>
P94 = 1204618859405030553363698323853833563350237788260488026770597375925396803921048656034405570407_<94>

Number: n N=15149386725281021123753962941845636012571236548033196437966015793924269592977295200949728825977617469721884804063340963115374974865790205783760408317288755574285706415903 ( 170 digits) SNFS difficulty: 175 digits. Divisors found: Sat May 16 20:13:23 2009 prp77 factor: 12576082971806871968069729416319272329315487489596105277919238868516031336329 Sat May 16 20:13:23 2009 prp94 factor: 1204618859405030553363698323853833563350237788260488026770597375925396803921048656034405570407 Sat May 16 20:13:23 2009 elapsed time 01:57:04 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 92.51 hours. Scaled time: 246.07 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_1_172_7 n: 15149386725281021123753962941845636012571236548033196437966015793924269592977295200949728825977617469721884804063340963115374974865790205783760408317288755574285706415903 m: 50000000000000000000000000000000000 deg: 5 c5: 88 c0: 265 skew: 1.25 type: snfs lss: 1 rlim: 5900000 alim: 5900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5900000/5900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2950000, 7750001) Primes: RFBsize:406429, AFBsize:406189, largePrimes:21211462 encountered Relations: rels:21323565, finalFF:723633 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2986877 hash collisions in 24112465 relations Msieve: matrix is 1043634 x 1043882 (273.1 MB) Total sieving time: 90.86 hours. Total relation processing time: 1.64 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,56,56,2.5,2.5,100000 total time: 92.51 hours. --------- CPU info (if available) ----------

May 16, 2009 (5th)

By Sinkiti Sibata / GGNFS / May 16, 2009
(55·10¹⁴³+71)/9 = 6(1)₁₄₂9_<144> = 17 · 29 · 991 · 4457 · 6493441453_<10> · 2838678287817353_<16> · C110
C110 = P41 · P69
P41 = 27019354239685156397295913693344519066703_<41>
P69 = 563496083463933782315403603663316451548918552533691438676317697210167_<69>

Number: 61119_143 N=15225300291787219991255509950617093567241683938470837984337757123021294767004829225327161644868299881682769401 ( 110 digits) SNFS difficulty: 145 digits. Divisors found: r1=27019354239685156397295913693344519066703 (pp41) r2=563496083463933782315403603663316451548918552533691438676317697210167 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 17.08 hours. Scaled time: 8.08 units (timescale=0.473). Factorization parameters were as follows: name: 61119_143 n: 15225300291787219991255509950617093567241683938470837984337757123021294767004829225327161644868299881682769401 m: 50000000000000000000000000000 deg: 5 c5: 88 c0: 355 skew: 1.32 type: snfs lss: 1 rlim: 1860000 alim: 1860000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1860000/1860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [930000, 2230001) Primes: RFBsize:139249, AFBsize:139185, largePrimes:3996264 encountered Relations: rels:4113629, finalFF:376850 Max relations in full relation-set: 28 Initial matrix: 278500 x 376850 with sparse part having weight 36482233. Pruned matrix : 244485 x 245941 with weight 20666563. Total sieving time: 15.21 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.59 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.3,2.3,100000 total time: 17.08 hours. --------- CPU info (if available) ----------

May 16, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 16, 2009
(53·10¹⁹⁸-17)/9 = 5(8)₁₉₇7_<199> = C199
C199 = P52 · P148
P52 = 3105261215890219980188797697842256974579853865273347_<52>
P148 = 1896423031580824744009636372699045793880183375458593621015135886801884722666025272281158636589101925037831403331081551847068185738937524060810693821_<148>

Number: 58887_198 N=5888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 ( 199 digits) SNFS difficulty: 199 digits. Divisors found: r1=3105261215890219980188797697842256974579853865273347 r2=1896423031580824744009636372699045793880183375458593621015135886801884722666025272281158636589101925037831403331081551847068185738937524060810693821 Version: Total time: 495.00 hours. Scaled time: 1183.05 units (timescale=2.390). Factorization parameters were as follows: n: 5888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 1000000000000000000000000000000000 deg: 6 c6: 53 c0: -17 skew: 0.83 type: snfs lss: 1 rlim: 20000000 alim: 20000000 lpbr: 29 lpba: 29 mfbr: 55 mfba: 55 rlambda: 2.6 alambda: 2.6 Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 55/55 Sieved rational special-q in [10000000, 20700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 35575862 Max relations in full relation-set: Initial matrix: Pruned matrix : 3176756 x 3177003 Total sieving time: 445.27 hours. Total relation processing time: 22.31 hours. Matrix solve time: 26.88 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: snfs,199,6,0,0,0,0,0,0,0,0,20000000,20000000,29,29,55,55,2.6,2.6,100000 total time: 495.00 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 16, 2009 (3rd)

By Dmitry Domanov / Msieve / May 16, 2009
(55·10¹⁶²+71)/9 = 6(1)₁₆₁9_<163> = 7 · C162
C162 = P41 · P58 · P64
P41 = 27343748654766962023770897524061237446659_<41>
P58 = 5056764184952869943581882885968674046825445552654199267029_<58>
P64 = 6313808207126857150929194815143949309287693135354451798881427847_<64>

N=873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017 ( 162 digits) SNFS difficulty: 164 digits. Divisors found: r1=27343748654766962023770897524061237446659 (pp41) r2=5056764184952869943581882885968674046825445552654199267029 (pp58) r3=6313808207126857150929194815143949309287693135354451798881427847 (pp64) Version: Msieve v. 1.41 Total time: 41.38 hours. Scaled time: 36.42 units (timescale=0.880). Factorization parameters were as follows: n: 873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017 m: 200000000000000000000000000000000 deg: 5 c5: 1375 c0: 568 skew: 0.84 type: snfs lss: 1 rlim: 3900000 alim: 3900000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3900000/3900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1950000, 4050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 712923 x 713171 Total sieving time: 39.93 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.91 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,164.000,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000 total time: 41.38 hours. --------- CPU info (if available) ----------

May 16, 2009 (2nd)

By matsui / GGNFS / May 16, 2009
8·10¹⁷⁸+3 = 8(0)₁₇₇3_<179> = 7 · 11 · 73 · 120504276263123_<15> · C162
C162 = P46 · P116
P46 = 1521121596498992083430684328800554217699357191_<46>
P116 = 77644377170813478936009808463885244242858683928639274087657213019286395263296774458233906745544656020639399572401451_<116>

N=118106538961237693228597702847944467131004093955164231095291492466633604287488596160101615398988803382502945819721906856579471463533012033849514923850146895684141 ( 162 digits) SNFS difficulty: 180 digits. Divisors found: r1=1521121596498992083430684328800554217699357191 (pp46) r2=77644377170813478936009808463885244242858683928639274087657213019286395263296774458233906745544656020639399572401451 (pp116) Version: GGNFS-0.77.1-20060722-nocona Total time: 118.65 hours. Scaled time: 259.61 units (timescale=2.188). Factorization parameters were as follows: n: 118106538961237693228597702847944467131004093955164231095291492466633604287488596160101615398988803382502945819721906856579471463533012033849514923850146895684141 m: 1000000000000000000000000000000000000 deg: 5 c5: 2 c0: 75 skew: 2.06 type: snfs lss: 1 rlim: 7100000 alim: 7100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7100000/7100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3550000, 5250001) Primes: RFBsize:483015, AFBsize:482366, largePrimes:17442103 encountered Relations: rels:17732404, finalFF:1229549 Max relations in full relation-set: 32 Initial matrix: 965446 x 1229548 with sparse part having weight 148799596. Pruned matrix : 762190 x 767081 with weight 115818416. Total sieving time: 108.34 hours. Total relation processing time: 0.28 hours. Matrix solve time: 9.76 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7100000,7100000,28,28,53,53,2.5,2.5,100000 total time: 118.65 hours.

Mar 16, 2009

By Serge Batalov / PFGW / Mar 15, 2009
(5·10⁶⁶³⁹⁴-17)/3 = 1(6)₆₆₃₉₃1_<66395> is PRP.

May 15, 2009 (3rd)

By Dmitry Domanov / GMP-ECM 6.2.3, Msieve v. 1.41, GGNFS-0.77.1-VC8 / May 15, 2009
(55·10¹⁹²+71)/9 = 6(1)₁₉₁9_<193> = 7² · 19 · 28211 · C186
C186 = P33 · P153
P33 = 287860258795288440499702779905657_<33>
P153 = 808295771108102506695396656539593972616330973723038986708273430564327994343724988972906260199977808554283757311321321457279161095184020165058222553689087_<153>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=989525659 Step 1 took 91250ms ********** Factor found in step 1: 287860258795288440499702779905657 Found probable prime factor of 33 digits: 287860258795288440499702779905657 Probable prime cofactor 808295771108102506695396656539593972616330973723038986708273430564327994343724988972906260199977808554283757311321321457279161095184020165058222553689087 has 153 digits

(49·10¹⁷⁰-13)/9 = 5(4)₁₆₉3_<171> = 3³ · 17 · 53 · 5027117 · C160
C160 = P61 · P100
P61 = 2692212159653272355339435109096075286883559301953867086090461_<61>
P100 = 1653623901550726337767533156447700441142090917636728902297814526133953699616039119659459695609726357_<100>

Number: 6 N=4451906375248151182830922835284818657113863806841579312202067690879499966017767766632869279766525410733659197053565189224887023373656337781407513933537157980577 ( 160 digits) SNFS difficulty: 171 digits. Divisors found: r1=2692212159653272355339435109096075286883559301953867086090461 (pp61) r2=1653623901550726337767533156447700441142090917636728902297814526133953699616039119659459695609726357 (pp100) Version: Msieve v. 1.41 Total time: 79.84 hours. Scaled time: 156.25 units (timescale=1.957). Factorization parameters were as follows: n: 4451906375248151182830922835284818657113863806841579312202067690879499966017767766632869279766525410733659197053565189224887023373656337781407513933537157980577 m: 10000000000000000000000000000000000 deg: 5 c5: 49 c0: -13 skew: 0.77 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 4950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 756235 x 756483 Total sieving time: 77.49 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.08 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 79.84 hours. --------- CPU info (if available) ----------

(55·10¹⁶⁵+71)/9 = 6(1)₁₆₄9_<166> = 809 · 3691 · 108263 · C155
C155 = P35 · P120
P35 = 24335341153262737407629933896579409_<35>
P120 = 776801609907481825359557101187910185903023150073711522354469400696299227987950943173477493221818097747365114068869669603_<120>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3179055233 Step 1 took 68563ms Step 2 took 22078ms ********** Factor found in step 2: 24335341153262737407629933896579409 Found probable prime factor of 35 digits: 24335341153262737407629933896579409 Probable prime cofactor 776801609907481825359557101187910185903023150073711522354469400696299227987950943173477493221818097747365114068869669603 has 120 digits

(55·10¹⁹⁷+71)/9 = 6(1)₁₉₆9_<198> = 18642536789_<11> · C188
C188 = P35 · P153
P35 = 57547309236684489528941761046601613_<35>
P153 = 569626452891159171398342923688370533308071766262310180490302207470807685125526248239176720252301776078743824072951071192362669399076391681375266653470367_<153>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=389729675 Step 1 took 332672ms ********** Factor found in step 1: 57547309236684489528941761046601613 Found probable prime factor of 35 digits: 57547309236684489528941761046601613 Probable prime cofactor 569626452891159171398342923688370533308071766262310180490302207470807685125526248239176720252301776078743824072951071192362669399076391681375266653470367 has 153 digits

5·10¹⁶⁸-9 = 4(9)₁₆₇1_<169> = 31 · 29150029 · 97690322401972470211_<20> · C140
C140 = P63 · P78
P63 = 285672459115302906984888083354597717349768178359030194770540009_<63>
P78 = 198266528819518056600744503449893297480133294347181748253063893651091266424791_<78>

Number: 1 N=56639286848126797554729386539227574885723785334536125536236873465330483256275559559736715759646622674484365026756974688483306430233854963119 ( 140 digits) SNFS difficulty: 169 digits. Divisors found: r1=285672459115302906984888083354597717349768178359030194770540009 (pp63) r2=198266528819518056600744503449893297480133294347181748253063893651091266424791 (pp78) Version: GGNFS-0.77.1-VC8 Total time: 52.63 hours. Scaled time: 50.58 units (timescale=0.961). Factorization parameters were as follows: n: 56639286848126797554729386539227574885723785334536125536236873465330483256275559559736715759646622674484365026756974688483306430233854963119 m: 5000000000000000000000000000000000 deg: 5 c5: 8 c0: -45 skew: 1.41 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 4450001) Primes: RFBsize:328964, AFBsize:327919, largePrimes:9912007 encountered Relations: rels:10182561, finalFF:745248 Max relations in full relation-set: 32 Initial matrix: 656948 x 745248 with sparse part having weight 81981595. Pruned matrix : 605955 x 609303 with weight 63712113. Total sieving time: 47.58 hours. Total relation processing time: 0.39 hours. Matrix solve time: 4.17 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 52.63 hours. --------- CPU info (if available) ----------

(55·10¹⁵⁹+71)/9 = 6(1)₁₅₈9_<160> = 17 · 368130319157_<12> · 123677208423467_<15> · C133
C133 = P36 · P48 · P50
P36 = 140978348475664396838504814127042339_<36>
P48 = 882572282190700517976402060539018250089665494407_<48>
P50 = 63456672439732865549259372993901595965810017344261_<50>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2455922270 Step 1 took 49813ms Step 2 took 16422ms ********** Factor found in step 2: 140978348475664396838504814127042339 Found probable prime factor of 36 digits: 140978348475664396838504814127042339 Composite cofactor 56005100215362762921524962760356855338997610012921755070987428408384155357213923636656407689048227 has 98 digits Number: 0 N=56005100215362762921524962760356855338997610012921755070987428408384155357213923636656407689048227 ( 98 digits) Divisors found: r1=882572282190700517976402060539018250089665494407 (pp48) r2=63456672439732865549259372993901595965810017344261 (pp50) Version: Msieve v. 1.41 Total time: 4.15 hours. Scaled time: 8.17 units (timescale=1.969). Factorization parameters were as follows: name: 0 n: 56005100215362762921524962760356855338997610012921755070987428408384155357213923636656407689048227 skew: 1563.26 # norm 4.73e+012 c5: 54720 c4: 420073014 c3: -981929555154 c2: -902696291016996 c1: 539606548664109961 c0: 133625764604402100645 # alpha -3.85 Y1: 6255630337 Y0: -3999587985258256558 # Murphy_E 4.32e-009 # M 7500094444286231710467509873971966573554565601358545473228276408641175903590409269742379495665611 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 159857 x 160093 Polynomial selection time: 0.29 hours. Total sieving time: 3.70 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 4.15 hours. --------- CPU info (if available) ----------

(55·10¹⁸⁸+71)/9 = 6(1)₁₈₇9_<189> = 21379 · 39133 · 3151970057_<10> · C171
C171 = P35 · C136
P35 = 23808035090930888675002054458419521_<35>
C136 = [9733835730442108411910371839197331283579776706732797283991862852256898234576047790599455636483601588124994915389202362114965362983239361_<136>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=751087292 Step 1 took 75563ms Step 2 took 22469ms ********** Factor found in step 2: 23808035090930888675002054458419521 Found probable prime factor of 35 digits: 23808035090930888675002054458419521 Composite cofactor 9733835730442108411910371839197331283579776706732797283991862852256898234576047790599455636483601588124994915389202362114965362983239361 has 136 digits

May 15, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 15, 2009
(55·10¹⁸³+71)/9 = 6(1)₁₈₂9_<184> = 211 · 2897 · 14843 · 78504742266311_<14> · 18923252562065045071433_<23> · 1456022502472854275881544383_<28> · C111
C111 = P53 · P59
P53 = 26506006175993381272829828763617837641121116742352467_<53>
P59 = 11747987680181600226218167193411018631966399612495045430693_<59>

Number: n N=311392234006387651672448081841093655775367230411377420724646687474507875782489096294534955481137814140026069631 ( 111 digits) Divisors found: r1=26506006175993381272829828763617837641121116742352467 (pp53) r2=11747987680181600226218167193411018631966399612495045430693 (pp59) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 15.22 hours. Scaled time: 40.16 units (timescale=2.639). Factorization parameters were as follows: name: KA_6_1_182_9 n: 311392234006387651672448081841093655775367230411377420724646687474507875782489096294534955481137814140026069631 Y0: -2584568069450941420360 Y1: 384958070083 c0: -4059072098339572523025137763 c1: 105158492379506668504759 c2: -2883980861159280569 c3: -33217032757935 c4: 172810416 c5: 2700 skew: 87047.99 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1600000, 2250001) Primes: RFBsize:230209, AFBsize:230270, largePrimes:16995536 encountered Relations: rels:15559641, finalFF:665605 Max relations in full relation-set: 28 Initial matrix: 460562 x 665605 with sparse part having weight 65940252. Pruned matrix : 307315 x 309681 with weight 37286889. Total sieving time: 13.61 hours. Total relation processing time: 0.63 hours. Matrix solve time: 0.50 hours. Total square root time: 0.48 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 15.22 hours. --------- CPU info (if available) ----------

(55·10¹⁶⁴+53)/9 = 6(1)₁₆₃7_<165> = 151 · 2449623037_<10> · 13672234223_<11> · 4175286873883_<13> · C131
C131 = P49 · P82
P49 = 4997494605967408149532708505482310328253201826819_<49>
P82 = 5791163563277687995964939570082543825557369323515164525575236980824238068315661321_<82>

Number: n N=28941308669755240703099761874611761902648796448592435335238186323844236163242374178690923009820090062849191275519712456825298767899 ( 131 digits) SNFS difficulty: 166 digits. Divisors found: r1=4997494605967408149532708505482310328253201826819 (pp49) r2=5791163563277687995964939570082543825557369323515164525575236980824238068315661321 (pp82) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 38.21 hours. Scaled time: 101.65 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_1_163_7 n: 28941308669755240703099761874611761902648796448592435335238186323844236163242374178690923009820090062849191275519712456825298767899 m: 1000000000000000000000000000000000 deg: 5 c5: 11 c0: 106 skew: 1.57 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [2050000, 4150001) Primes: RFBsize:289774, AFBsize:289728, largePrimes:16159564 encountered Relations: rels:16219905, finalFF:774173 Max relations in full relation-set: 28 Initial matrix: 579567 x 774173 with sparse part having weight 90821724. Pruned matrix : 504359 x 507320 with weight 60248084. Total sieving time: 35.33 hours. Total relation processing time: 0.60 hours. Matrix solve time: 2.09 hours. Total square root time: 0.20 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,28,28,56,56,2.4,2.4,100000 total time: 38.21 hours. --------- CPU info (if available) ----------

(16·10¹⁶⁹-7)/9 = 1(7)_169<170> = 224494463 · 786434162050807_<15> · C147
C147 = P67 · P80
P67 = 3487303178927087329591975815409665587670114255927538052409984233861_<67>
P80 = 28874851741200275794024069838665289918909310930811410451426125078495030526283477_<80>

Number: n N=100695362268136064504090189001146777329779870588394993991707548409930165374487468529253744023227795557950486006149084859840889633580942941548214697 ( 147 digits) SNFS difficulty: 170 digits. Divisors found: Fri May 15 18:14:48 2009 prp67 factor: 3487303178927087329591975815409665587670114255927538052409984233861 Fri May 15 18:14:48 2009 prp80 factor: 28874851741200275794024069838665289918909310930811410451426125078495030526283477 Fri May 15 18:14:48 2009 elapsed time 01:16:27 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 44.07 hours. Scaled time: 115.29 units (timescale=2.616). Factorization parameters were as follows: name: KA_1_7_169 n: 100695362268136064504090189001146777329779870588394993991707548409930165374487468529253744023227795557950486006149084859840889633580942941548214697 m: 10000000000000000000000000000000000 deg: 5 c5: 8 c0: -35 skew: 1.34 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2450000, 4945807) Primes: RFBsize:341992, AFBsize:342818, largePrimes:16487133 encountered Relations: rels:15756849, finalFF:691854 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1756427 hash collisions in 17765435 relations Msieve: matrix is 838205 x 838453 (222.9 MB) Total sieving time: 43.41 hours. Total relation processing time: 0.67 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000 total time: 44.07 hours. --------- CPU info (if available) ----------

(55·10¹⁵⁵+71)/9 = 6(1)₁₅₄9_<156> = 23 · 58111 · 58519711 · 8773380623124748443600727_<25> · C117
C117 = P36 · P82
P36 = 143979646441272912798751233599595527_<36>
P82 = 6185342438048729794328561855111197190980660408468874396459980926568055950707673417_<82>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 890563417348457120832571640459891732891698128325691856818376277007924756340699090705920238580843477520126626410005759 (117 digits) Using B1=2812000, B2=4281592780, polynomial Dickson(6), sigma=962927361 Step 1 took 31293ms Step 2 took 11045ms ********** Factor found in step 2: 143979646441272912798751233599595527 Found probable prime factor of 36 digits: 143979646441272912798751233599595527 Probable prime cofactor 6185342438048729794328561855111197190980660408468874396459980926568055950707673417 has 82 digits

(22·10¹⁹⁸-1)/3 = 7(3)_198<199> = 7 · 947 · C196
C196 = P91 · P105
P91 = 2882509691785175067582718426919249615849023053552230314201221226189350602539682348570293787_<91>
P105 = 383780258372884261144561599255815402930959690519198066403669312732520597025168652619394376800947167879971_<105>

Number: n N=1106250314275657464675416100970483230250917684919796852215014833811032332679639965806808467843314728214411424548700155880726102479006386081359682204455171720219238698647357570272037009101423040177 ( 196 digits) SNFS difficulty: 201 digits. Divisors found: Sat May 16 00:29:16 2009 prp91 factor: 2882509691785175067582718426919249615849023053552230314201221226189350602539682348570293787 Sat May 16 00:29:16 2009 prp105 factor: 383780258372884261144561599255815402930959690519198066403669312732520597025168652619394376800947167879971 Sat May 16 00:29:16 2009 elapsed time 13:18:45 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 48.70 hours. Scaled time: 98.07 units (timescale=2.014). Factorization parameters were as follows: name: KA_7_3_198 n: 1106250314275657464675416100970483230250917684919796852215014833811032332679639965806808467843314728214411424548700155880726102479006386081359682204455171720219238698647357570272037009101423040177 m: 10000000000000000000000000000000000000000 deg: 5 c5: 11 c0: -50 skew: 1.35 type: snfs lss: 1 rlim: 15700000 alim: 15700000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 15700000/15700000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved special-q in [7850000, 18449990) Primes: RFBsize:1013012, AFBsize:1013131, largePrimes:1338580 encountered Relations: rels:492627, finalFF:2135 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 4991232 hash collisions in 39498402 relations Msieve: matrix is 2901304 x 2901551 (788.9 MB) Total sieving time: 48.29 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,15700000,15700000,29,29,56,56,2.6,2.6,100000 total time: 48.70 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.95 BogoMIPS (lpj=2830476) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448) Total of 4 processors activated (22643.65 BogoMIPS).

May 15, 2009

By Sinkiti Sibata / GGNFS, Msieve / May 15, 2009
(55·10¹⁴⁷+71)/9 = 6(1)₁₄₆9_<148> = 198049777 · 1191274607893_<13> · 3445375456503515469833_<22> · C106
C106 = P35 · P72
P35 = 38467029705765547003621767930288053_<35>
P72 = 195437873678482374142781791356471424100324561115046333227355307258309471_<72>

Number: 61119_147 N=7517914492421835984058082848772797746445706638101076514609535759322165343395314387564217846404742848049963 ( 106 digits) SNFS difficulty: 149 digits. Divisors found: r1=38467029705765547003621767930288053 (pp35) r2=195437873678482374142781791356471424100324561115046333227355307258309471 (pp72) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 30.08 hours. Scaled time: 14.26 units (timescale=0.474). Factorization parameters were as follows: name: 61119_147 n: 7517914492421835984058082848772797746445706638101076514609535759322165343395314387564217846404742848049963 m: 200000000000000000000000000000 deg: 5 c5: 1375 c0: 568 skew: 0.84 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 3300001) Primes: RFBsize:162662, AFBsize:163732, largePrimes:4529351 encountered Relations: rels:4808079, finalFF:401513 Max relations in full relation-set: 28 Initial matrix: 326461 x 401513 with sparse part having weight 45599410. Pruned matrix : 298915 x 300611 with weight 32209704. Total sieving time: 26.26 hours. Total relation processing time: 0.31 hours. Matrix solve time: 3.41 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 30.08 hours. --------- CPU info (if available) ----------

(55·10¹³⁰+71)/9 = 6(1)₁₂₉9_<131> = 3² · 1031 · 931529 · 190631621 · 8946032747_<10> · C103
C103 = P50 · P53
P50 = 57792086304242895797761529441075115537051264545837_<50>
P53 = 71734624341105295983203643470137196510267861291590811_<53>

Number: 61119_130 N=4145693600923600439019225896942391349240772136386757922097820672747695605767505311568861222153157503807 ( 103 digits) SNFS difficulty: 131 digits. Divisors found: r1=57792086304242895797761529441075115537051264545837 (pp50) r2=71734624341105295983203643470137196510267861291590811 (pp53) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 4.08 hours. Scaled time: 8.50 units (timescale=2.085). Factorization parameters were as follows: name: 61119_130 n: 4145693600923600439019225896942391349240772136386757922097820672747695605767505311568861222153157503807 m: 100000000000000000000000000 deg: 5 c5: 55 c0: 71 skew: 1.05 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1050001) Primes: RFBsize:85714, AFBsize:85671, largePrimes:2883022 encountered Relations: rels:2799303, finalFF:196462 Max relations in full relation-set: 0 Initial matrix: 171451 x 196462 with sparse part having weight 12761126. Pruned matrix : 162923 x 163844 with weight 9315655. Total sieving time: 3.59 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.36 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 4.08 hours. --------- CPU info (if available) ----------

(2·10²⁰⁰+61)/9 = (2)₁₉₉9_<200> = 83 · 2467 · 184979095439_<12> · 5333768258713_<13> · 1512398390473675457_<19> · 26701944159591873857_<20> · C133
C133 = P43 · P91
P43 = 1497861280087620589909136478546959010780631_<43>
P91 = 1818455870333425172805446104788266873468151731202279729908506761054955089871521334546301933_<91>

Number: 22229_200 N=2723794637720472432204933599865783189450593732942352213812665665109521854121902291932603177585967974672262187391031649342980554259723 ( 133 digits) Divisors found: r1=1497861280087620589909136478546959010780631 (pp43) r2=1818455870333425172805446104788266873468151731202279729908506761054955089871521334546301933 (pp91) Version: Msieve-1.40 Total time: 227.95 hours. Scaled time: 577.64 units (timescale=2.534). Factorization parameters were as follows: name: 22229_200 # Murphy_E = 5.494297e-11, selected by Jeff Gilchrist n: 2723794637720472432204933599865783189450593732942352213812665665109521854121902291932603177585967974672262187391031649342980554259723 Y0: -34083099048428297234644474 Y1: 489835657370593 c0: -9259140913743911300061266453723475 c1: 62185006038906236125531442825 c2: 5782097466008962033351 c3: -160600625715381517 c4: 100331183196 c5: 59220 skew: 932771.02 type: gnfs # selected mechanically rlim: 11400000 alim: 11400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.6 alambda: 2.6 Factor base limits: 11400000/11400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved algebraic special-q in [5700000, 12700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1656585 x 1656833 Total sieving time: 227.95 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,132,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11400000,11400000,28,28,54,54,2.6,2.6,100000 total time: 227.95 hours. --------- CPU info (if available) ----------

May 14, 2009 (5th)

By Wataru Sakai / Msieve / May 14, 2009
2·10¹⁹⁷-3 = 1(9)₁₉₆7_<198> = 7 · 229 · C195
C195 = P71 · P124
P71 = 45003138917615480291651707486311828111477830485732830843961796036510537_<71>
P124 = 2772385807556537886278044630282889688258769602192237958344592362510261040148261536809278151720138041797820440202530552797127_<124>

Number: 19997_197 N=124766063630692451653150343106674984404242046163443543356207111665626949469744229569557080474111041796631316281971303805364940736119775421085464753587024329382407985028072364316905801621958827199 ( 195 digits) SNFS difficulty: 197 digits. Divisors found: r1=45003138917615480291651707486311828111477830485732830843961796036510537 r2=2772385807556537886278044630282889688258769602192237958344592362510261040148261536809278151720138041797820440202530552797127 Version: Total time: 744.51 hours. Scaled time: 1495.72 units (timescale=2.009). Factorization parameters were as follows: n: 124766063630692451653150343106674984404242046163443543356207111665626949469744229569557080474111041796631316281971303805364940736119775421085464753587024329382407985028072364316905801621958827199 m: 2000000000000000000000000000000000000000 deg: 5 c5: 25 c0: -12 skew: 0.86 type: snfs lss: 1 rlim: 13900000 alim: 13900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13900000/13900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6950000, 14750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2364522 x 2364770 Total sieving time: 744.51 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,197,5,0,0,0,0,0,0,0,0,13900000,13900000,28,28,55,55,2.5,2.5,100000 total time: 744.51 hours. --------- CPU info (if available) ----------

May 14, 2009 (4th)

By Erik Branger / GGNFS, Msieve / May 14, 2009
(55·10¹⁴⁹+71)/9 = 6(1)₁₄₈9_<150> = 1451 · 16735128726520447_<17> · C131
C131 = P56 · P76
P56 = 23212997212751433550558533812477592022876236828704855219_<56>
P76 = 1084157780944424495342154432830333239216149136776625618872855134155864499233_<76>

Number: 61119_149 N=25166551547245705068022667865324015802313222330807856045784508390828702589330659816586726877460696078270591924272438604665201547027 ( 131 digits) SNFS difficulty: 151 digits. Divisors found: r1=23212997212751433550558533812477592022876236828704855219 (pp56) r2=1084157780944424495342154432830333239216149136776625618872855134155864499233 (pp76) Version: Msieve v. 1.41 Total time: 19.18 hours. Scaled time: 13.08 units (timescale=0.682). Factorization parameters were as follows: n: 25166551547245705068022667865324015802313222330807856045784508390828702589330659816586726877460696078270591924272438604665201547027 m: 1000000000000000000000000000000 deg: 5 c5: 11 c0: 142 skew: 1.67 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 429819 x 430067 Total sieving time: 18.45 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.52 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 19.18 hours. --------- CPU info (if available) ----------

May 14, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 14, 2009
(53·10¹⁶⁶-71)/9 = 5(8)₁₆₅1_<167> = 3 · 19 · 29 · 83 · 240857467 · 11060457607_<11> · 20894699998037_<14> · C130
C130 = P43 · P88
P43 = 5424508418994216438894842882597473125698917_<43>
P88 = 1421519024674072529801317548921990745200160059101495179565493543560830040916204609073619_<88>

Number: 58881_166 N=7711041917104953726782529594857675992009409630005014615924347870515549294274391649540185622317721217959229856759607475749281570623 ( 130 digits) SNFS difficulty: 167 digits. Divisors found: r1=5424508418994216438894842882597473125698917 r2=1421519024674072529801317548921990745200160059101495179565493543560830040916204609073619 Version: Total time: 38.60 hours. Scaled time: 92.10 units (timescale=2.386). Factorization parameters were as follows: n: 7711041917104953726782529594857675992009409630005014615924347870515549294274391649540185622317721217959229856759607475749281570623 m: 1000000000000000000000000000000000 deg: 5 c5: 530 c0: -71 skew: 0.67 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2700000, 5800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10253930 Max relations in full relation-set: Initial matrix: Pruned matrix : 927795 x 928043 Total sieving time: 35.06 hours. Total relation processing time: 1.54 hours. Matrix solve time: 1.86 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,51,51,2.4,2.4,100000 total time: 38.60 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 14, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / May 14, 2009
(55·10¹³⁸+71)/9 = 6(1)₁₃₇9_<139> = 7 · 19 · 1093 · 12097 · 61109474407_<11> · C119
C119 = P48 · P72
P48 = 289391643646385040320441989989840975406837712761_<48>
P72 = 196506156640222333226584793107921238684003927617477930888307670421176329_<72>

Number: 61119_138 N=56867239656747940880840066906923991757368581244680647382966913848232606251219165722336772704148144736484366229434434369 ( 119 digits) SNFS difficulty: 140 digits. Divisors found: r1=289391643646385040320441989989840975406837712761 (pp48) r2=196506156640222333226584793107921238684003927617477930888307670421176329 (pp72) Version: Msieve-1.40 Total time: 4.20 hours. Scaled time: 5.04 units (timescale=1.199). Factorization parameters were as follows: n: 56867239656747940880840066906923991757368581244680647382966913848232606251219165722336772704148144736484366229434434369 m: 5000000000000000000000000000 deg: 5 c5: 88 c0: 355 skew: 1.32 type: snfs lss: 1 rlim: 1530000 alim: 1530000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1530000/1530000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [765000, 1515001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 255878 x 256126 Total sieving time: 4.04 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,140.000,5,0,0,0,0,0,0,0,0,1530000,1530000,26,26,48,48,2.3,2.3,75000 total time: 4.20 hours. --------- CPU info (if available) ----------

(55·10¹⁴⁵+71)/9 = 6(1)₁₄₄9_<146> = 3 · 59167396759_<11> · C135
C135 = P37 · P45 · P54
P37 = 1570742754374861168243498981181423131_<37>
P45 = 281156538114519295288982577419736057441054869_<45>
P54 = 779584528197470392113982771350216223141302084755533973_<54>

Number: 61119_145 N=344283701602467697819545543720316890177993480146959973341192007240028560242683202522108961092181053589124501883180281265657472736105347 ( 135 digits) SNFS difficulty: 146 digits. Divisors found: r1=1570742754374861168243498981181423131 (pp37) r2=281156538114519295288982577419736057441054869 (pp45) r3=779584528197470392113982771350216223141302084755533973 (pp54) Version: Msieve-1.40 Total time: 8.17 hours. Scaled time: 9.79 units (timescale=1.199). Factorization parameters were as follows: n: 344283701602467697819545543720316890177993480146959973341192007240028560242683202522108961092181053589124501883180281265657472736105347 m: 100000000000000000000000000000 deg: 5 c5: 55 c0: 71 skew: 1.05 type: snfs lss: 1 rlim: 1950000 alim: 1950000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1950000/1950000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [975000, 2375001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 360259 x 360506 Total sieving time: 7.81 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.16 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000 total time: 8.17 hours. --------- CPU info (if available) ----------

(47·10¹⁷⁰-11)/9 = 5(2)₁₆₉1_<171> = 9095447 · C164
C164 = P52 · P112
P52 = 8325089385253334517465388703578602396233093909125411_<52>
P112 = 6896716845965064599580999289660546133794620672918628965695890490643567789344672084630394151336043454230418416713_<112>

Number: 52221_170 N=57415784207441615813079029785146592819706631485205974178313855517185930743395263830598124778498761217807351548771844003073430280251451327485303605443715105175394043 ( 164 digits) SNFS difficulty: 171 digits. Divisors found: r1=8325089385253334517465388703578602396233093909125411 (pp52) r2=6896716845965064599580999289660546133794620672918628965695890490643567789344672084630394151336043454230418416713 (pp112) Version: Msieve-1.40 Total time: 52.56 hours. Scaled time: 91.40 units (timescale=1.739). Factorization parameters were as follows: n: 57415784207441615813079029785146592819706631485205974178313855517185930743395263830598124778498761217807351548771844003073430280251451327485303605443715105175394043 m: 10000000000000000000000000000000000 deg: 5 c5: 47 c0: -11 skew: 0.75 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 5250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 973380 x 973628 Total sieving time: 51.04 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.23 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 52.56 hours. --------- CPU info (if available) ----------

May 14, 2009

By Sinkiti Sibata / Msieve / May 14, 2009
(55·10¹²⁰+71)/9 = 6(1)₁₁₉9_<121> = 7 · 19² · 113 · 5351 · 101641 · 94005377 · C99
C99 = P35 · P65
P35 = 10612628407459289169056826061471913_<35>
P65 = 39441821288257056813672440441195723701568061228860695191005265959_<65>

Wed May 13 18:40:18 2009 Msieve v. 1.41 Wed May 13 18:40:18 2009 random seeds: 299d5308 80c0a959 Wed May 13 18:40:18 2009 factoring 418581393045689377984564463862677455714402642533209998362505773916333663494054907215380225573509567 (99 digits) Wed May 13 18:40:19 2009 searching for 15-digit factors Wed May 13 18:40:20 2009 commencing quadratic sieve (99-digit input) Wed May 13 18:40:20 2009 using multiplier of 43 Wed May 13 18:40:20 2009 using 32kb Intel Core sieve core Wed May 13 18:40:20 2009 sieve interval: 36 blocks of size 32768 Wed May 13 18:40:20 2009 processing polynomials in batches of 6 Wed May 13 18:40:20 2009 using a sieve bound of 2605661 (95294 primes) Wed May 13 18:40:20 2009 using large prime bound of 390849150 (28 bits) Wed May 13 18:40:20 2009 using double large prime bound of 2921571209356950 (43-52 bits) Wed May 13 18:40:20 2009 using trial factoring cutoff of 52 bits Wed May 13 18:40:20 2009 polynomial 'A' values have 13 factors Thu May 14 02:36:01 2009 95402 relations (23456 full + 71946 combined from 1419148 partial), need 95390 Thu May 14 02:36:03 2009 begin with 1442604 relations Thu May 14 02:36:04 2009 reduce to 248255 relations in 11 passes Thu May 14 02:36:04 2009 attempting to read 248255 relations Thu May 14 02:36:08 2009 recovered 248255 relations Thu May 14 02:36:08 2009 recovered 237014 polynomials Thu May 14 02:36:09 2009 attempting to build 95402 cycles Thu May 14 02:36:09 2009 found 95402 cycles in 6 passes Thu May 14 02:36:09 2009 distribution of cycle lengths: Thu May 14 02:36:09 2009 length 1 : 23456 Thu May 14 02:36:09 2009 length 2 : 16740 Thu May 14 02:36:09 2009 length 3 : 15775 Thu May 14 02:36:09 2009 length 4 : 13018 Thu May 14 02:36:09 2009 length 5 : 9827 Thu May 14 02:36:09 2009 length 6 : 6604 Thu May 14 02:36:09 2009 length 7 : 4044 Thu May 14 02:36:09 2009 length 9+: 5938 Thu May 14 02:36:09 2009 largest cycle: 21 relations Thu May 14 02:36:09 2009 matrix is 95294 x 95402 (25.9 MB) with weight 6407269 (67.16/col) Thu May 14 02:36:09 2009 sparse part has weight 6407269 (67.16/col) Thu May 14 02:36:11 2009 filtering completed in 3 passes Thu May 14 02:36:11 2009 matrix is 90901 x 90965 (24.9 MB) with weight 6155977 (67.67/col) Thu May 14 02:36:11 2009 sparse part has weight 6155977 (67.67/col) Thu May 14 02:36:11 2009 saving the first 48 matrix rows for later Thu May 14 02:36:11 2009 matrix is 90853 x 90965 (14.9 MB) with weight 4832527 (53.13/col) Thu May 14 02:36:11 2009 sparse part has weight 3372544 (37.08/col) Thu May 14 02:36:11 2009 matrix includes 64 packed rows Thu May 14 02:36:11 2009 using block size 36386 for processor cache size 1024 kB Thu May 14 02:36:12 2009 commencing Lanczos iteration Thu May 14 02:36:12 2009 memory use: 14.7 MB Thu May 14 02:37:08 2009 lanczos halted after 1438 iterations (dim = 90847) Thu May 14 02:37:08 2009 recovered 15 nontrivial dependencies Thu May 14 02:37:10 2009 prp35 factor: 10612628407459289169056826061471913 Thu May 14 02:37:10 2009 prp65 factor: 39441821288257056813672440441195723701568061228860695191005265959 Thu May 14 02:37:10 2009 elapsed time 07:56:52

May 13, 2009 (9th)

By Dmitry Domanov / GGNFS-0.77.1-VC8, Msieve / May 13, 2009
(55·10¹⁰⁸+71)/9 = 6(1)₁₀₇9_<109> = 7³ · 397 · 166507538969_<12> · C93
C93 = P39 · P54
P39 = 795809090623752224301704775278817744859_<39>
P54 = 338682498969665965499901130193421539222442974752330159_<54>

Number: 2 N=269526611515229771672836695269380413385510175130506157107543076549664233927981393987792902581 ( 93 digits) SNFS difficulty: 110 digits. Divisors found: r1=795809090623752224301704775278817744859 (pp39) r2=338682498969665965499901130193421539222442974752330159 (pp54) Version: GGNFS-0.77.1-VC8 Total time: 0.71 hours. Scaled time: 1.40 units (timescale=1.963). Factorization parameters were as follows: n: 269526611515229771672836695269380413385510175130506157107543076549664233927981393987792902581 m: 5000000000000000000000 deg: 5 c5: 88 c0: 355 skew: 1.32 type: snfs lss: 1 rlim: 490000 alim: 490000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 490000/490000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [245000, 395001) Primes: RFBsize:40766, AFBsize:40609, largePrimes:1258579 encountered Relations: rels:1276691, finalFF:183902 Max relations in full relation-set: 32 Initial matrix: 81441 x 183902 with sparse part having weight 8158930. Pruned matrix : 54054 x 54525 with weight 1896575. Total sieving time: 0.66 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,490000,490000,25,25,44,44,2.2,2.2,50000 total time: 0.71 hours. --------- CPU info (if available) ----------

(55·10¹²⁵+71)/9 = 6(1)₁₂₄9_<126> = 1926187 · 2077388651851_<13> · C108
C108 = P47 · P62
P47 = 13802361609306560051417136173839078839962476523_<47>
P62 = 11064978550966575301700323020187377468908938943339427779145269_<62>

Number: 3 N=152722835159661589179909953116879454214067758007163553303317915183692361104914415723369724182544041419019687 ( 108 digits) SNFS difficulty: 126 digits. Divisors found: r1=13802361609306560051417136173839078839962476523 (pp47) r2=11064978550966575301700323020187377468908938943339427779145269 (pp62) Version: GGNFS-0.77.1-VC8 Total time: 1.93 hours. Scaled time: 3.81 units (timescale=1.976). Factorization parameters were as follows: n: 152722835159661589179909953116879454214067758007163553303317915183692361104914415723369724182544041419019687 m: 10000000000000000000000000 deg: 5 c5: 55 c0: 71 skew: 1.05 type: snfs lss: 1 rlim: 910000 alim: 910000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 910000/910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [455000, 805001) Primes: RFBsize:72026, AFBsize:71959, largePrimes:2514719 encountered Relations: rels:2404279, finalFF:195014 Max relations in full relation-set: 32 Initial matrix: 144051 x 195014 with sparse part having weight 16220392. Pruned matrix : 128954 x 129738 with weight 7826179. Total sieving time: 1.75 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.05 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000 total time: 1.93 hours. --------- CPU info (if available) ----------

(55·10¹²⁷+71)/9 = 6(1)₁₂₆9_<128> = 3 · 17 · 269 · 164411016323_<12> · C113
C113 = P54 · P60
P54 = 147564695883632722993402372598585997374827274660357417_<54>
P60 = 183604931912357354495039990669131942492925879496484038120011_<60>

Number: 4 N=27093605940382105687802024807602056821259075656855857209595838697644304254924346891285469235754267974673999971587 ( 113 digits) SNFS difficulty: 129 digits. Divisors found: r1=147564695883632722993402372598585997374827274660357417 (pp54) r2=183604931912357354495039990669131942492925879496484038120011 (pp60) Version: Msieve v. 1.41 Total time: 2.05 hours. Scaled time: 2.75 units (timescale=1.339). Factorization parameters were as follows: n: 27093605940382105687802024807602056821259075656855857209595838697644304254924346891285469235754267974673999971587 m: 20000000000000000000000000 deg: 5 c5: 1375 c0: 568 skew: 0.84 type: snfs lss: 1 rlim: 1010000 alim: 1010000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1010000/1010000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [505000, 905001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 150245 x 150479 Total sieving time: 1.95 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,129.000,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000 total time: 2.05 hours. --------- CPU info (if available) ----------

(55·10¹³⁴+71)/9 = 6(1)₁₃₃9_<135> = 5425331 · C129
C129 = P56 · P73
P56 = 49822004090217615607527790375081111028061432525658809403_<56>
P73 = 2260855195620981138777563605147208165708944206584407558122279483171277583_<73>

Number: 5 N=112640336803618269762916052700030857308265820299463961021200570271401157111171854972740116890768712749712618660706805006203512949 ( 129 digits) SNFS difficulty: 136 digits. Divisors found: r1=49822004090217615607527790375081111028061432525658809403 (pp56) r2=2260855195620981138777563605147208165708944206584407558122279483171277583 (pp73) Version: Msieve v. 1.41 Total time: 3.38 hours. Scaled time: 6.61 units (timescale=1.957). Factorization parameters were as follows: n: 112640336803618269762916052700030857308265820299463961021200570271401157111171854972740116890768712749712618660706805006203512949 m: 1000000000000000000000000000 deg: 5 c5: 11 c0: 142 skew: 1.67 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 196615 x 196847 Total sieving time: 3.22 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 3.38 hours. --------- CPU info (if available) ----------

May 13, 2009 (8th)

By Tyler Cadigan / GGNFS, Msieve / May 13, 2009
6·10¹⁹²+1 = 6(0)₁₉₁1_<193> = 7 · 99079 · 687912079 · C179
C179 = P70 · P109
P70 = 2915419952598811618594940160413805922953111384734672751972710929408139_<70>
P109 = 4313576840393877505883357285400035595676725490320331778252232358628296531245916896568438767438261380374823357_<109>

Number: 60001_192 N=12575887987552449949026242858572851364527613573509060923551620410457482729565243389228910414519077788326664190901048863112517318053854082566295455325857182378946464323168683102623 ( 179 digits) SNFS difficulty: 193 digits. Divisors found: r1=2915419952598811618594940160413805922953111384734672751972710929408139 (pp70) r2=4313576840393877505883357285400035595676725490320331778252232358628296531245916896568438767438261380374823357 (pp109) Version: Msieve-1.40 Total time: 386.28 hours. Scaled time: 982.69 units (timescale=2.544). Factorization parameters were as follows: n: 12575887987552449949026242858572851364527613573509060923551620410457482729565243389228910414519077788326664190901048863112517318053854082566295455325857182378946464323168683102623 m: 200000000000000000000000000000000000000 deg: 5 c5: 75 c0: 4 skew: 0.56 type: snfs lss: 1 rlim: 11700000 alim: 11700000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 11700000/11700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5850000, 10850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1767676 x 1767924 Total sieving time: 378.49 hours. Total relation processing time: 0.41 hours. Matrix solve time: 7.10 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,193.000,5,0,0,0,0,0,0,0,0,11700000,11700000,28,28,55,55,2.5,2.5,100000 total time: 386.28 hours. --------- CPU info (if available) ----------

May 13, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / May 13, 2009
(55·10¹³⁹+71)/9 = 6(1)₁₃₈9_<140> = 3² · 759229 · 105356774741_<12> · 48705511430143_<14> · 1883619831516079_<16> · C93
C93 = P44 · P50
P44 = 86804442778701194714084453798411031294437723_<44>
P50 = 10659310159320433870594507542608353345250244368549_<50>

Wed May 13 14:06:03 2009 Msieve v. 1.41 Wed May 13 14:06:03 2009 random seeds: 34888b00 964c2405 Wed May 13 14:06:03 2009 factoring 925275478785158917225656192117079539340868018513415131273758526283118667747065881088140373927 (93 digits) Wed May 13 14:06:04 2009 searching for 15-digit factors Wed May 13 14:06:06 2009 commencing quadratic sieve (93-digit input) Wed May 13 14:06:06 2009 using multiplier of 15 Wed May 13 14:06:06 2009 using 32kb Intel Core sieve core Wed May 13 14:06:06 2009 sieve interval: 36 blocks of size 32768 Wed May 13 14:06:06 2009 processing polynomials in batches of 6 Wed May 13 14:06:06 2009 using a sieve bound of 1956901 (72864 primes) Wed May 13 14:06:06 2009 using large prime bound of 244612625 (27 bits) Wed May 13 14:06:06 2009 using double large prime bound of 1256787622996125 (42-51 bits) Wed May 13 14:06:06 2009 using trial factoring cutoff of 51 bits Wed May 13 14:06:06 2009 polynomial 'A' values have 12 factors Wed May 13 17:07:46 2009 73280 relations (18342 full + 54938 combined from 1001546 partial), need 72960 Wed May 13 17:07:48 2009 begin with 1019888 relations Wed May 13 17:07:49 2009 reduce to 189126 relations in 12 passes Wed May 13 17:07:49 2009 attempting to read 189126 relations Wed May 13 17:07:52 2009 recovered 189126 relations Wed May 13 17:07:52 2009 recovered 173044 polynomials Wed May 13 17:07:52 2009 attempting to build 73280 cycles Wed May 13 17:07:52 2009 found 73280 cycles in 6 passes Wed May 13 17:07:52 2009 distribution of cycle lengths: Wed May 13 17:07:52 2009 length 1 : 18342 Wed May 13 17:07:52 2009 length 2 : 12923 Wed May 13 17:07:52 2009 length 3 : 12297 Wed May 13 17:07:52 2009 length 4 : 9931 Wed May 13 17:07:52 2009 length 5 : 7447 Wed May 13 17:07:52 2009 length 6 : 4947 Wed May 13 17:07:52 2009 length 7 : 3129 Wed May 13 17:07:52 2009 length 9+: 4264 Wed May 13 17:07:52 2009 largest cycle: 18 relations Wed May 13 17:07:53 2009 matrix is 72864 x 73280 (19.4 MB) with weight 4798388 (65.48/col) Wed May 13 17:07:53 2009 sparse part has weight 4798388 (65.48/col) Wed May 13 17:07:54 2009 filtering completed in 3 passes Wed May 13 17:07:54 2009 matrix is 69225 x 69289 (18.4 MB) with weight 4546351 (65.61/col) Wed May 13 17:07:54 2009 sparse part has weight 4546351 (65.61/col) Wed May 13 17:07:54 2009 saving the first 48 matrix rows for later Wed May 13 17:07:54 2009 matrix is 69177 x 69289 (11.9 MB) with weight 3640733 (52.54/col) Wed May 13 17:07:54 2009 sparse part has weight 2716755 (39.21/col) Wed May 13 17:07:54 2009 matrix includes 64 packed rows Wed May 13 17:07:54 2009 using block size 27715 for processor cache size 1024 kB Wed May 13 17:07:55 2009 commencing Lanczos iteration Wed May 13 17:07:55 2009 memory use: 11.3 MB Wed May 13 17:08:29 2009 lanczos halted after 1096 iterations (dim = 69175) Wed May 13 17:08:29 2009 recovered 18 nontrivial dependencies Wed May 13 17:08:29 2009 prp44 factor: 86804442778701194714084453798411031294437723 Wed May 13 17:08:29 2009 prp50 factor: 10659310159320433870594507542608353345250244368549 Wed May 13 17:08:29 2009 elapsed time 03:02:26

(55·10¹²²+71)/9 = 6(1)₁₂₁9_<123> = 2139290106271226863_<19> · C105
C105 = P43 · P62
P43 = 5373828558294265105721640099799107187217633_<43>
P62 = 53157762248322536159642656786976043318598797786328241167792961_<62>

Number: 61119_122 N=285660700865052406937603796147704614656446087367273326746205050617928636405919093004427741173180992481313 ( 105 digits) SNFS difficulty: 124 digits. Divisors found: r1=5373828558294265105721640099799107187217633 (pp43) r2=53157762248322536159642656786976043318598797786328241167792961 (pp62) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 4.07 hours. Scaled time: 1.92 units (timescale=0.473). Factorization parameters were as follows: name: 61119_122 n: 285660700865052406937603796147704614656446087367273326746205050617928636405919093004427741173180992481313 m: 2000000000000000000000000 deg: 5 c5: 1375 c0: 568 skew: 0.84 type: snfs lss: 1 rlim: 840000 alim: 840000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 840000/840000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [420000, 820001) Primes: RFBsize:66890, AFBsize:67446, largePrimes:1430103 encountered Relations: rels:1423767, finalFF:171226 Max relations in full relation-set: 28 Initial matrix: 134403 x 171226 with sparse part having weight 8895848. Pruned matrix : 120784 x 121520 with weight 4851384. Total sieving time: 3.84 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.13 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000 total time: 4.07 hours. --------- CPU info (if available) ----------

May 13, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / May 13, 2009
(38·10¹⁹⁶-11)/9 = 4(2)₁₉₅1_<197> = 41 · C196
C196 = P51 · P145
P51 = 838649704654846390758515578850272712034860490204961_<51>
P145 = 1227938545005281377336927487713597735223128756351156783641718045398180364148362046277704501731373166079193454606684278099220646885720543931030821_<145>

Number: n N=1029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981 ( 196 digits) SNFS difficulty: 198 digits. Divisors found: Wed May 13 08:29:26 2009 prp51 factor: 838649704654846390758515578850272712034860490204961 Wed May 13 08:29:26 2009 prp145 factor: 1227938545005281377336927487713597735223128756351156783641718045398180364148362046277704501731373166079193454606684278099220646885720543931030821 Wed May 13 08:29:26 2009 elapsed time 07:26:30 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 45.69 hours. Scaled time: 92.01 units (timescale=2.014). Factorization parameters were as follows: name: KA_4_2_195_1 n: 1029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981 m: 2000000000000000000000000000000000000000 deg: 5 c5: 95 c0: -88 skew: 0.98 type: snfs lss: 1 rlim: 14200000 alim: 14200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 14200000/14200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [7100000, 17600069) Primes: RFBsize:922193, AFBsize:921099, largePrimes:21624209 encountered Relations: rels:22687579, finalFF:1832439 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3063498 hash collisions in 25110169 relations Msieve: matrix is 2255039 x 2255287 (612.2 MB) Total sieving time: 45.26 hours. Total relation processing time: 0.43 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,198,5,0,0,0,0,0,0,0,0,14200000,14200000,28,28,56,56,2.5,2.5,100000 total time: 45.69 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.95 BogoMIPS (lpj=2830476) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448) Total of 4 processors activated (22643.65 BogoMIPS).

(55·10¹⁷¹+53)/9 = 6(1)₁₇₀7_<172> = 3 · 10037 · C168
C168 = P46 · P123
P46 = 1564288375667914117144174724299318185064610611_<46>
P123 = 129741281454502009424231502334110360678149501887013003964661212991492932260928953098054019152165699509735690212465942370977_<123>

Number: n N=202952778423536618216303381193288536120059483614330680187011760190997014749131915615924782010265720537714161306868291026904158317927372425728508223277576670024612636947 ( 168 digits) SNFS difficulty: 172 digits. Divisors found: Wed May 13 18:27:32 2009 prp46 factor: 1564288375667914117144174724299318185064610611 Wed May 13 18:27:32 2009 prp123 factor: 129741281454502009424231502334110360678149501887013003964661212991492932260928953098054019152165699509735690212465942370977 Wed May 13 18:27:32 2009 elapsed time 01:53:42 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 62.51 hours. Scaled time: 166.95 units (timescale=2.671). Factorization parameters were as follows: name: KA_6_1_170_7 n: 202952778423536618216303381193288536120059483614330680187011760190997014749131915615924782010265720537714161306868291026904158317927372425728508223277576670024612636947 m: 10000000000000000000000000000000000 deg: 5 c5: 550 c0: 53 skew: 0.63 type: snfs lss: 1 rlim: 5300000 alim: 5300000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5300000/5300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2650000, 6195757) Primes: RFBsize:367900, AFBsize:368503, largePrimes:17829043 encountered Relations: rels:17580473, finalFF:723415 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2219364 hash collisions in 19608042 relations Msieve: matrix is 928670 x 928918 (249.1 MB) Total sieving time: 61.63 hours. Total relation processing time: 0.87 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,28,28,56,56,2.4,2.4,100000 total time: 62.51 hours. --------- CPU info (if available) ----------

May 13, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 13, 2009
(55·10¹³⁶+71)/9 = 6(1)₁₃₅9_<137> = 3 · 317 · 14615383 · 75201397 · C119
C119 = P34 · P86
P34 = 1350876569924994979685157442302889_<34>
P86 = 43280063054364300687962637464433987423404953530263290263897966741530468685681866670571_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3080153974 Step 1 took 7820ms Step 2 took 8057ms ********** Factor found in step 2: 1350876569924994979685157442302889 Found probable prime factor of 34 digits: 1350876569924994979685157442302889 Probable prime cofactor 43280063054364300687962637464433987423404953530263290263897966741530468685681866670571 has 86 digits

(55·10¹⁴⁶+71)/9 = 6(1)₁₄₅9_<147> = 31 · 639127301537443_<15> · C131
C131 = P37 · P95
P37 = 1202940587193747624789004146323185267_<37>
P95 = 25640526478973531362019019068776774655905775461468850331552024081456281866972753004198890605529_<95>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=129212221 Step 1 took 7868ms Step 2 took 4637ms ********** Factor found in step 2: 1202940587193747624789004146323185267 Found probable prime factor of 37 digits: 1202940587193747624789004146323185267 Probable prime cofactor has 95 digits

(55·10¹¹¹+71)/9 = 6(1)₁₁₀9_<112> = 17 · 23 · C110
C110 = P52 · P58
P52 = 8496004963601417069043767504345188776275945693950363_<52>
P58 = 1839622298813323932133290065541136712345074736938839826043_<58>

SNFS difficulty: 112 digits. Divisors found: r1=8496004963601417069043767504345188776275945693950363 (pp52) r2=1839622298813323932133290065541136712345074736938839826043 (pp58) Version: Msieve v. 1.41 Total time: 0.58 hours. Scaled time: 1.58 units (timescale=2.726). Factorization parameters were as follows: n: 15629440181869849389030974708724069337880079568059107701051435066780335322534811025859619210002841716396703609 m: 10000000000000000000000 deg: 5 c5: 550 c0: 71 skew: 0.66 type: snfs lss: 1 rlim: 530000 alim: 530000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 530000/530000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [265000, 465001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 52949 x 53178 Total sieving time: 0.55 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000 total time: 0.58 hours.

(55·10²⁰³+71)/9 = 6(1)₂₀₂9_<204> = 1493 · 50741 · 148669 · C191
C191 = P31 · C161
P31 = 1538483614307183777646719386573_<31>
C161 = [35268586554235955747475441610403345347488406143285663324380184048565519635843557694050030383279827772428163249553044073162469530126538634244471616142594370633599_<161>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3878632275 Step 1 took 12345ms Step 2 took 6401ms ********** Factor found in step 2: 1538483614307183777646719386573 Found probable prime factor of 31 digits: 1538483614307183777646719386573 Composite cofactor has 161 digits

May 13, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 13, 2009
2·10¹⁷⁶-1 = 1(9)_176<177> = 257 · 156577 · 16506330678736007_<17> · 6963592316914968855505993_<25> · C128
C128 = P58 · P71
P58 = 2638173759595778891884183100234637053647717064980325343311_<58>
P71 = 16390100988022968074152500639629002445679211540543545306742330563674831_<71>

Number: 19999_176 N=43239934343727043867038071858195868131316110066819744096987416719312710840761544224861895751661857201711227598866960845844905441 ( 128 digits) SNFS difficulty: 176 digits. Divisors found: r1=2638173759595778891884183100234637053647717064980325343311 r2=16390100988022968074152500639629002445679211540543545306742330563674831 Version: Total time: 43.15 hours. Scaled time: 103.12 units (timescale=2.390). Factorization parameters were as follows: n: 43239934343727043867038071858195868131316110066819744096987416719312710840761544224861895751661857201711227598866960845844905441 m: 100000000000000000000000000000000000 deg: 5 c5: 20 c0: -1 skew: 0.55 type: snfs lss: 1 rlim: 6800000 alim: 6800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6800000/6800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3400000, 6300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 17790087 Max relations in full relation-set: Initial matrix: Pruned matrix : 1183787 x 1184034 Total sieving time: 37.04 hours. Total relation processing time: 2.59 hours. Matrix solve time: 3.21 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000 total time: 43.15 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 13, 2009 (3rd)

By Markus Tervooren / msieve 1.41, ggnfs / May 13, 2009
(53·10¹⁶⁵-17)/9 = 5(8)₁₆₄7_<166> = 7 · 639157301 · 683426917 · 6327944358701217101_<19> · C129
C129 = P48 · P82
P48 = 105286041996195116463905211753052493939462823619_<48>
P82 = 2890693427093959193600294796557751916681459460044103037225919482688402201684641967_<82>

N=304349669563139773775039543739558410678652128462622576347732269179402880997642153306106637637619365345888591599963791904886218573 ( 129 digits) SNFS difficulty: 166 digits. Divisors found: r1=105286041996195116463905211753052493939462823619 (pp48) r2=2890693427093959193600294796557751916681459460044103037225919482688402201684641967 (pp82) Version: Msieve-1.39 Total time: 23.99 hours. Scaled time: 55.15 units (timescale=2.299). Factorization parameters were as follows: n: 304349669563139773775039543739558410678652128462622576347732269179402880997642153306106637637619365345888591599963791904886218573 m: 1000000000000000000000000000000000 deg: 5 c5: 53 c0: -17 skew: 0.80 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 26 lpba: 26 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 51/51 Sieved rational special-q in [2100000, 4500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 688361 x 688609 Total sieving time: 23.27 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.55 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,26,26,51,51,2.4,2.4,200000 total time: 23.99 hours. --------- CPU info (if available) ---------- [ 0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.331180] CPU2: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.428163] CPU3: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init) [ 0.083917] Calibrating delay using timer specific routine.. 6004.15 BogoMIPS (lpj=12008301) [ 0.156009] Calibrating delay using timer specific routine.. 5999.99 BogoMIPS (lpj=11999993) [ 0.248015] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000012) [ 0.347710] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000008) [ 0.435711] Total of 4 processors activated (24004.15 BogoMIPS).

May 13, 2009 (2nd)

By Erik Branger / GMP-ECM, Msieve / May 13, 2009
(10²⁴⁵-7)/3 = (3)₂₄₄1_<245> = 97 · 66751 · 3258371 · 1403863703183_<13> · 2249810655289_<13> · 81791825300240873_<17> · 145142221366577384926667_<24> · 31324445949473317700096188175894333_<35> · C133
C133 = P39 · P45 · P50
P39 = 489315672447162785103946339787661019447_<39>
P45 = 222569895610081321713872192753638833118459541_<45>
P50 = 12351940072441846049300946746600885270935752027829_<50>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 1345211973340636127176790697467331273618032323820765030845459707299234006881987792073875316307596244915355092769177331580459819511583 (133 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3233337030 Step 1 took 61137ms Step 2 took 34851ms ********** Factor found in step 2: 489315672447162785103946339787661019447 Found probable prime factor of 39 digits: 489315672447162785103946339787661019447 Composite cofactor 2749170012505361993924940218503304494061357616514900432821055688206426386787140909263442566489 has 94 digits Tue May 12 16:49:26 2009 Msieve v. 1.41 Tue May 12 16:49:26 2009 random seeds: f1649488 eee56b85 Tue May 12 16:49:26 2009 factoring 2749170012505361993924940218503304494061357616514900432821055688206426386787140909263442566489 (94 digits) Tue May 12 16:49:27 2009 searching for 15-digit factors Tue May 12 16:49:28 2009 commencing quadratic sieve (94-digit input) Tue May 12 16:49:28 2009 using multiplier of 1 Tue May 12 16:49:28 2009 using 32kb Intel Core sieve core Tue May 12 16:49:28 2009 sieve interval: 36 blocks of size 32768 Tue May 12 16:49:28 2009 processing polynomials in batches of 6 Tue May 12 16:49:28 2009 using a sieve bound of 2018827 (75294 primes) Tue May 12 16:49:28 2009 using large prime bound of 270522818 (28 bits) Tue May 12 16:49:28 2009 using double large prime bound of 1506492608811942 (42-51 bits) Tue May 12 16:49:28 2009 using trial factoring cutoff of 51 bits Tue May 12 16:49:28 2009 polynomial 'A' values have 12 factors Tue May 12 19:42:45 2009 75640 relations (18903 full + 56737 combined from 1060241 partial), need 75390 Tue May 12 19:42:48 2009 begin with 1079144 relations Tue May 12 19:42:49 2009 reduce to 194509 relations in 11 passes Tue May 12 19:42:49 2009 attempting to read 194509 relations Tue May 12 19:42:52 2009 recovered 194509 relations Tue May 12 19:42:52 2009 recovered 174919 polynomials Tue May 12 19:42:53 2009 attempting to build 75640 cycles Tue May 12 19:42:53 2009 found 75640 cycles in 6 passes Tue May 12 19:42:53 2009 distribution of cycle lengths: Tue May 12 19:42:53 2009 length 1 : 18903 Tue May 12 19:42:53 2009 length 2 : 13565 Tue May 12 19:42:53 2009 length 3 : 12840 Tue May 12 19:42:53 2009 length 4 : 10239 Tue May 12 19:42:53 2009 length 5 : 7608 Tue May 12 19:42:53 2009 length 6 : 5067 Tue May 12 19:42:53 2009 length 7 : 3115 Tue May 12 19:42:53 2009 length 9+: 4303 Tue May 12 19:42:53 2009 largest cycle: 20 relations Tue May 12 19:42:53 2009 matrix is 75294 x 75640 (18.9 MB) with weight 4642777 (61.38/col) Tue May 12 19:42:53 2009 sparse part has weight 4642777 (61.38/col) Tue May 12 19:42:54 2009 filtering completed in 3 passes Tue May 12 19:42:54 2009 matrix is 71370 x 71434 (17.9 MB) with weight 4398060 (61.57/col) Tue May 12 19:42:54 2009 sparse part has weight 4398060 (61.57/col) Tue May 12 19:42:54 2009 saving the first 48 matrix rows for later Tue May 12 19:42:54 2009 matrix is 71322 x 71434 (10.5 MB) with weight 3349481 (46.89/col) Tue May 12 19:42:54 2009 sparse part has weight 2318382 (32.45/col) Tue May 12 19:42:54 2009 matrix includes 64 packed rows Tue May 12 19:42:54 2009 using block size 28573 for processor cache size 2048 kB Tue May 12 19:42:55 2009 commencing Lanczos iteration Tue May 12 19:42:55 2009 memory use: 10.7 MB Tue May 12 19:43:22 2009 lanczos halted after 1130 iterations (dim = 71320) Tue May 12 19:43:22 2009 recovered 15 nontrivial dependencies Tue May 12 19:43:22 2009 prp45 factor: 222569895610081321713872192753638833118459541 Tue May 12 19:43:22 2009 prp50 factor: 12351940072441846049300946746600885270935752027829 Tue May 12 19:43:22 2009 elapsed time 02:53:56

May 13, 2009

Factorizations of 611...119 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 12, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 11, 2009
(55·10¹⁵⁸+53)/9 = 6(1)₁₅₇7_<159> = 17 · 4817497834280673583_<19> · C139
C139 = P56 · P84
P56 = 17845553710717112864759785999618398828238960930529700031_<56>
P84 = 418138062769178038646403383540644184918563093786817713598293397086549042213175848237_<84>

Number: n N=7461905257642570205274359759519501514193898474760211147148201732868313154587524623931779179230011032717598088072376762527591935829590195347 ( 139 digits) SNFS difficulty: 160 digits. Divisors found: Mon May 11 01:35:01 2009 prp56 factor: 17845553710717112864759785999618398828238960930529700031 Mon May 11 01:35:01 2009 prp84 factor: 418138062769178038646403383540644184918563093786817713598293397086549042213175848237 Mon May 11 01:35:01 2009 elapsed time 00:43:35 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 26.47 hours. Scaled time: 68.98 units (timescale=2.606). Factorization parameters were as follows: name: KA_6_1_157_7 n: 7461905257642570205274359759519501514193898474760211147148201732868313154587524623931779179230011032717598088072376762527591935829590195347 m: 50000000000000000000000000000000 deg: 5 c5: 88 c0: 265 skew: 1.25 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1650000, 3231931) Primes: RFBsize:236900, AFBsize:236768, largePrimes:13344150 encountered Relations: rels:12314752, finalFF:423174 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1315446 hash collisions in 14066940 relations Msieve: matrix is 609139 x 609387 (163.0 MB) Total sieving time: 26.17 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,28,28,56,56,2.4,2.4,100000 total time: 26.47 hours. --------- CPU info (if available) ----------

(55·10¹⁵²+53)/9 = 6(1)₁₅₁7_<153> = 19 · 59 · 227 · 659 · 12695518245859_<14> · C132
C132 = P55 · P77
P55 = 7068361314994357655785488053712469413994760160307524653_<55>
P77 = 40610105745920779918481121272161456452030286435210027784502911521712533819907_<77>

Number: n N=287046900452296523635214596698421367210854311194270084376888166052944430800517935676949223976641000358837008264491447433837664667271 ( 132 digits) SNFS difficulty: 155 digits. Divisors found: Mon May 11 14:21:24 2009 prp55 factor: 7068361314994357655785488053712469413994760160307524653 Mon May 11 14:21:24 2009 prp77 factor: 40610105745920779918481121272161456452030286435210027784502911521712533819907 Mon May 11 14:21:24 2009 elapsed time 00:25:14 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 14.91 hours. Scaled time: 38.08 units (timescale=2.554). Factorization parameters were as follows: name: KA_6_1_151_7 n: 287046900452296523635214596698421367210854311194270084376888166052944430800517935676949223976641000358837008264491447433837664667271 m: 5000000000000000000000000000000 deg: 5 c5: 44 c0: 1325 skew: 1.98 type: snfs lss: 1 rlim: 2700000 alim: 2700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2700000/2700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1350000, 2250257) Primes: RFBsize:196645, AFBsize:196816, largePrimes:11996756 encountered Relations: rels:11284515, finalFF:436714 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 914717 hash collisions in 12009197 relations Msieve: matrix is 430294 x 430542 (115.0 MB) Total sieving time: 14.70 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,28,28,56,56,2.4,2.4,100000 total time: 14.91 hours. --------- CPU info (if available) ----------

(55·10¹⁶⁹+53)/9 = 6(1)₁₆₈7_<170> = 21385781 · 1709871325461113_<16> · C148
C148 = P38 · P110
P38 = 31499273936242556516634609465971955509_<38>
P110 = 53055583145099933520947588688085961040800233395621622150497267775458366053416556199130127742788741791063315421_<110>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 1671212347334596219507410428017889758975124908091594236923391998388037186811384996722745868763892908306829644401101534483453918223449576156245604289 (148 digits) Using B1=1798000, B2=2140281790, polynomial Dickson(6), sigma=2177163353 Step 1 took 27627ms Step 2 took 8830ms ********** Factor found in step 2: 31499273936242556516634609465971955509 Found probable prime factor of 38 digits: 31499273936242556516634609465971955509 Probable prime cofactor 53055583145099933520947588688085961040800233395621622150497267775458366053416556199130127742788741791063315421 has 110 digits

By Robert Backstrom / GGNFS, Msieve / May 12, 2009
(55·10¹⁶¹+53)/9 = 6(1)₁₆₀7_<162> = 13 · 97 · 113 · 76625767327269088745587943_<26> · C131
C131 = P59 · P73
P59 = 25937588457776918008836386172560311496435019969223053253357_<59>
P73 = 2157854800973617411073781544796855937311836707863709108700798479647760419_<73>

Number: n N=55969549779291807578331999389155335060385717795888554665336739968324394289490377698401886225152663948359880548781879323856843476583 ( 131 digits) SNFS difficulty: 162 digits. Divisors found: r1=25937588457776918008836386172560311496435019969223053253357 (pp59) r2=2157854800973617411073781544796855937311836707863709108700798479647760419 (pp73) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 30.09 hours. Scaled time: 79.41 units (timescale=2.639). Factorization parameters were as follows: name: KA_6_1_160_7 n: 55969549779291807578331999389155335060385717795888554665336739968324394289490377698401886225152663948359880548781879323856843476583 m: 100000000000000000000000000000000 deg: 5 c5: 550 c0: 53 skew: 0.63 type: snfs lss: 1 rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1800000, 3500001) Primes: RFBsize:256726, AFBsize:256777, largePrimes:14804714 encountered Relations: rels:14493415, finalFF:613981 Max relations in full relation-set: 28 Initial matrix: 513570 x 613981 with sparse part having weight 68840197. Pruned matrix : 472743 x 475374 with weight 50744989. Total sieving time: 27.82 hours. Total relation processing time: 0.47 hours. Matrix solve time: 1.59 hours. Total square root time: 0.20 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,56,56,2.4,2.4,100000 total time: 30.09 hours. --------- CPU info (if available) ----------

May 12, 2009 (3rd)

By Markus Tervooren / msieve 1.41, lattice siever (64bit/asm) / May 12, 2009
4·10²¹²+9 = 4(0)₂₁₁9_<213> = 1057477 · 1719841 · 2162154127181111154546903829_<28> · 77175797637606010161708971689_<29> · C145
C145 = P52 · P93
P52 = 1746066645189561080367807342423137376428492594383633_<52>
P93 = 754870008751017698161582119509494539523940082054318759700337322475860229316028590649214989769_<93>

N=1318053343734104086960715457060197971758523491913154564415959276396377517554642471068781120825155195038852382956221675167363777490332564956050777 ( 145 digits) Divisors found: r1=1746066645189561080367807342423137376428492594383633 (pp52) r2=754870008751017698161582119509494539523940082054318759700337322475860229316028590649214989769 (pp93) Version: Msieve-1.39 Total time: 669.60 hours. Scaled time: 1536.06 units (timescale=2.294). Factorization parameters were as follows: name: k2 n: 1318053343734104086960715457060197971758523491913154564415959276396377517554642471068781120825155195038852382956221675167363777490332564956050777 skew: 605055.65 # norm 5.12e+19 c5: 208980 c4: -133514539821 c3: 487140766392643324 c2: 51625269952217739580169 c1: -93618180336738951476232970236 c0: -5793741626299058757465782496791055 # alpha -5.97 Y1: 75003706647780877 Y0: -5753953870187591385948231242 # Murphy_E 1.08e-11 # M 800290932745809964278718692174746748367343098838672689905478792809784630966191593908087431020740065478694759215807174794065578110867414729744866 type: gnfs rlim: 22000000 alim: 22000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 22000000/22000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [11000000, 34000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2408276 x 2408524 Total sieving time: 657.69 hours. Total relation processing time: 0.47 hours. Matrix solve time: 10.99 hours. Time per square root: 0.44 hours. Prototype def-par.txt line would be: gnfs,144,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,22000000,22000000,28,28,52,52,2.6,2.6,200000 total time: 669.60 hours. --------- CPU info (if available) ---------- [ 0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.331180] CPU2: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.428163] CPU3: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init) [ 0.083917] Calibrating delay using timer specific routine.. 6004.15 BogoMIPS (lpj=12008301) [ 0.156009] Calibrating delay using timer specific routine.. 5999.99 BogoMIPS (lpj=11999993) [ 0.248015] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000012) [ 0.347710] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000008) [ 0.435711] Total of 4 processors activated (24004.15 BogoMIPS).

May 12, 2009 (2nd)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 11, 2009
10²⁴⁵-9 = (9)₂₄₄1_<245> = 40974399286914864833693_<23> · C223
C223 = P34 · C189
P34 = 5715411392874728022457273897097329_<34>
C189 = [427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003_<189>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1951669128 Step 1 took 441703ms Step 2 took 107218ms ********** Factor found in step 2: 5715411392874728022457273897097329 Found probable prime factor of 34 digits: 5715411392874728022457273897097329 Composite cofactor 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003 has 189 digits

By Dmitry Domanov / GGNFS, msieve / May 12, 2009
7·10¹⁸⁷-9 = 6(9)₁₈₆1_<188> = 461 · 923371 · 473554153625182489683337_<24> · 4690476648547345168326374837406127_<34> · C122
C122 = P51 · P72
P51 = 132247220045280786396912011749138627359993288829687_<51>
P72 = 559819090026885770857005522645932550743849730325918357433966783937734297_<72>

Tue May 05 13:21:24 2009 Msieve v. 1.41 Tue May 05 13:21:24 2009 random seeds: 796211e0 c7c337b8 Tue May 05 13:21:24 2009 factoring 74034518384334417089817067969336107865932654799596895823511091185372389129149571176376292605794361402236374912345491675039 (122 digits) Tue May 05 13:21:24 2009 searching for 15-digit factors Tue May 05 13:21:26 2009 commencing number field sieve (122-digit input) Tue May 05 13:21:26 2009 R0: -338415587465557897385425 Tue May 05 13:21:26 2009 R1: 25169084109103 Tue May 05 13:21:26 2009 A0: -19554326764852222388358345552 Tue May 05 13:21:26 2009 A1: 2374031057583121590915716 Tue May 05 13:21:26 2009 A2: 89638104094787780664 Tue May 05 13:21:26 2009 A3: -53426264244359 Tue May 05 13:21:26 2009 A4: -7014396274 Tue May 05 13:21:26 2009 A5: 16680 Tue May 05 13:21:26 2009 skew 105853.63, size 1.087434e-011, alpha -5.584116, combined = 2.285903e-010 Tue May 05 13:21:26 2009 Tue May 05 13:21:26 2009 commencing relation filtering Tue May 05 13:21:26 2009 commencing duplicate removal, pass 1 Tue May 05 13:23:26 2009 found 3680062 hash collisions in 14352905 relations Tue May 05 13:23:49 2009 added 62650 free relations Tue May 05 13:23:49 2009 commencing duplicate removal, pass 2 Tue May 05 13:24:22 2009 found 4221914 duplicates and 10193640 unique relations Tue May 05 13:24:22 2009 memory use: 106.6 MB Tue May 05 13:24:22 2009 reading rational ideals above 7929856 Tue May 05 13:24:22 2009 reading algebraic ideals above 7929856 Tue May 05 13:24:22 2009 commencing singleton removal, pass 1 Tue May 05 13:25:56 2009 relations with 0 large ideals: 319804 Tue May 05 13:25:56 2009 relations with 1 large ideals: 1789543 Tue May 05 13:25:56 2009 relations with 2 large ideals: 3700610 Tue May 05 13:25:56 2009 relations with 3 large ideals: 3267043 Tue May 05 13:25:56 2009 relations with 4 large ideals: 1046919 Tue May 05 13:25:56 2009 relations with 5 large ideals: 11575 Tue May 05 13:25:56 2009 relations with 6 large ideals: 58146 Tue May 05 13:25:56 2009 relations with 7+ large ideals: 0 Tue May 05 13:25:56 2009 10193640 relations and about 9206532 large ideals Tue May 05 13:25:56 2009 commencing singleton removal, pass 2 Tue May 05 13:27:29 2009 found 3746144 singletons Tue May 05 13:27:29 2009 current dataset: 6447496 relations and about 4826112 large ideals Tue May 05 13:27:29 2009 commencing singleton removal, pass 3 Tue May 05 13:28:35 2009 found 907584 singletons Tue May 05 13:28:35 2009 current dataset: 5539912 relations and about 3868151 large ideals Tue May 05 13:28:35 2009 commencing singleton removal, pass 4 Tue May 05 13:29:33 2009 found 254745 singletons Tue May 05 13:29:33 2009 current dataset: 5285167 relations and about 3608888 large ideals Tue May 05 13:29:33 2009 commencing singleton removal, final pass Tue May 05 13:30:30 2009 memory use: 81.1 MB Tue May 05 13:30:30 2009 commencing in-memory singleton removal Tue May 05 13:30:30 2009 begin with 5285167 relations and 3822070 unique ideals Tue May 05 13:30:35 2009 reduce to 4716125 relations and 3242297 ideals in 13 passes Tue May 05 13:30:35 2009 max relations containing the same ideal: 33 Tue May 05 13:30:36 2009 reading rational ideals above 720000 Tue May 05 13:30:36 2009 reading algebraic ideals above 720000 Tue May 05 13:30:36 2009 commencing singleton removal, final pass Tue May 05 13:31:36 2009 keeping 3940660 ideals with weight <= 20, new excess is 380477 Tue May 05 13:31:40 2009 memory use: 128.6 MB Tue May 05 13:31:40 2009 commencing in-memory singleton removal Tue May 05 13:31:41 2009 begin with 4717910 relations and 3940660 unique ideals Tue May 05 13:31:48 2009 reduce to 4695435 relations and 3909770 ideals in 13 passes Tue May 05 13:31:48 2009 max relations containing the same ideal: 20 Tue May 05 13:31:51 2009 removing 982639 relations and 810483 ideals in 172156 cliques Tue May 05 13:31:51 2009 commencing in-memory singleton removal Tue May 05 13:31:51 2009 begin with 3712796 relations and 3909770 unique ideals Tue May 05 13:31:55 2009 reduce to 3585555 relations and 2966547 ideals in 9 passes Tue May 05 13:31:55 2009 max relations containing the same ideal: 20 Tue May 05 13:31:57 2009 removing 740278 relations and 568122 ideals in 172156 cliques Tue May 05 13:31:58 2009 commencing in-memory singleton removal Tue May 05 13:31:58 2009 begin with 2845277 relations and 2966547 unique ideals Tue May 05 13:32:00 2009 reduce to 2743763 relations and 2292206 ideals in 8 passes Tue May 05 13:32:00 2009 max relations containing the same ideal: 19 Tue May 05 13:32:01 2009 removing 74922 relations and 64719 ideals in 10203 cliques Tue May 05 13:32:02 2009 commencing in-memory singleton removal Tue May 05 13:32:02 2009 begin with 2668841 relations and 2292206 unique ideals Tue May 05 13:32:03 2009 reduce to 2667656 relations and 2226298 ideals in 5 passes Tue May 05 13:32:03 2009 max relations containing the same ideal: 19 Tue May 05 13:32:03 2009 relations with 0 large ideals: 28132 Tue May 05 13:32:03 2009 relations with 1 large ideals: 191693 Tue May 05 13:32:03 2009 relations with 2 large ideals: 536697 Tue May 05 13:32:03 2009 relations with 3 large ideals: 801502 Tue May 05 13:32:03 2009 relations with 4 large ideals: 682034 Tue May 05 13:32:03 2009 relations with 5 large ideals: 329226 Tue May 05 13:32:03 2009 relations with 6 large ideals: 86297 Tue May 05 13:32:03 2009 relations with 7+ large ideals: 12075 Tue May 05 13:32:03 2009 commencing 2-way merge Tue May 05 13:32:05 2009 reduce to 1695103 relation sets and 1253745 unique ideals Tue May 05 13:32:05 2009 commencing full merge Tue May 05 13:32:27 2009 memory use: 100.0 MB Tue May 05 13:32:27 2009 found 827118 cycles, need 767945 Tue May 05 13:32:27 2009 weight of 767945 cycles is about 53824455 (70.09/cycle) Tue May 05 13:32:27 2009 distribution of cycle lengths: Tue May 05 13:32:27 2009 1 relations: 74022 Tue May 05 13:32:27 2009 2 relations: 78780 Tue May 05 13:32:27 2009 3 relations: 82503 Tue May 05 13:32:27 2009 4 relations: 78536 Tue May 05 13:32:27 2009 5 relations: 74402 Tue May 05 13:32:27 2009 6 relations: 67129 Tue May 05 13:32:27 2009 7 relations: 60620 Tue May 05 13:32:27 2009 8 relations: 53361 Tue May 05 13:32:27 2009 9 relations: 45757 Tue May 05 13:32:27 2009 10+ relations: 152835 Tue May 05 13:32:27 2009 heaviest cycle: 17 relations Tue May 05 13:32:27 2009 commencing cycle optimization Tue May 05 13:32:29 2009 start with 4650542 relations Tue May 05 13:32:39 2009 pruned 148029 relations Tue May 05 13:32:39 2009 memory use: 118.4 MB Tue May 05 13:32:39 2009 distribution of cycle lengths: Tue May 05 13:32:39 2009 1 relations: 74022 Tue May 05 13:32:39 2009 2 relations: 80948 Tue May 05 13:32:39 2009 3 relations: 86351 Tue May 05 13:32:39 2009 4 relations: 81424 Tue May 05 13:32:39 2009 5 relations: 77632 Tue May 05 13:32:39 2009 6 relations: 69023 Tue May 05 13:32:39 2009 7 relations: 62318 Tue May 05 13:32:39 2009 8 relations: 53892 Tue May 05 13:32:39 2009 9 relations: 45856 Tue May 05 13:32:39 2009 10+ relations: 136479 Tue May 05 13:32:39 2009 heaviest cycle: 17 relations Tue May 05 13:32:41 2009 RelProcTime: 643 Tue May 05 13:32:41 2009 Tue May 05 13:32:41 2009 commencing linear algebra Tue May 05 13:32:41 2009 read 767945 cycles Tue May 05 13:32:43 2009 cycles contain 2401694 unique relations Tue May 05 13:33:28 2009 read 2401694 relations Tue May 05 13:33:32 2009 using 20 quadratic characters above 134216802 Tue May 05 13:33:44 2009 building initial matrix Tue May 05 13:34:13 2009 memory use: 275.5 MB Tue May 05 13:34:15 2009 read 767945 cycles Tue May 05 13:34:29 2009 matrix is 767716 x 767945 (216.1 MB) with weight 72678072 (94.64/col) Tue May 05 13:34:29 2009 sparse part has weight 51274069 (66.77/col) Tue May 05 13:34:42 2009 filtering completed in 3 passes Tue May 05 13:34:42 2009 matrix is 765071 x 765271 (215.7 MB) with weight 72511181 (94.75/col) Tue May 05 13:34:42 2009 sparse part has weight 51186251 (66.89/col) Tue May 05 13:34:46 2009 read 765271 cycles Tue May 05 13:36:32 2009 matrix is 765071 x 765271 (215.7 MB) with weight 72511181 (94.75/col) Tue May 05 13:36:32 2009 sparse part has weight 51186251 (66.89/col) Tue May 05 13:36:32 2009 saving the first 48 matrix rows for later Tue May 05 13:36:33 2009 matrix is 765023 x 765271 (208.1 MB) with weight 57393419 (75.00/col) Tue May 05 13:36:33 2009 sparse part has weight 49962643 (65.29/col) Tue May 05 13:36:33 2009 matrix includes 64 packed rows Tue May 05 13:36:33 2009 using block size 65536 for processor cache size 6144 kB Tue May 05 13:36:38 2009 commencing Lanczos iteration (4 threads) Tue May 05 13:36:38 2009 memory use: 223.6 MB Tue May 05 14:19:37 2009 lanczos halted after 12100 iterations (dim = 765022) Tue May 05 14:19:38 2009 recovered 31 nontrivial dependencies Tue May 05 14:19:38 2009 BLanczosTime: 2817 Tue May 05 14:19:38 2009 Tue May 05 14:19:38 2009 commencing square root phase Tue May 05 14:19:38 2009 reading relations for dependency 1 Tue May 05 14:19:39 2009 read 382671 cycles Tue May 05 14:19:39 2009 cycles contain 1485452 unique relations Tue May 05 14:20:40 2009 read 1485452 relations Tue May 05 14:20:47 2009 multiplying 1199326 relations Tue May 05 14:23:36 2009 multiply complete, coefficients have about 52.81 million bits Tue May 05 14:23:38 2009 initial square root is modulo 38250617 Tue May 05 14:27:55 2009 reading relations for dependency 2 Tue May 05 14:27:55 2009 read 382694 cycles Tue May 05 14:27:56 2009 cycles contain 1487123 unique relations Tue May 05 14:28:56 2009 read 1487123 relations Tue May 05 14:29:03 2009 multiplying 1199644 relations Tue May 05 14:31:51 2009 multiply complete, coefficients have about 52.83 million bits Tue May 05 14:31:53 2009 initial square root is modulo 38414923 Tue May 05 14:36:09 2009 sqrtTime: 991 Tue May 05 14:36:09 2009 prp51 factor: 132247220045280786396912011749138627359993288829687 Tue May 05 14:36:09 2009 prp72 factor: 559819090026885770857005522645932550743849730325918357433966783937734297 Tue May 05 14:36:09 2009 elapsed time 01:14:45

2·10¹⁷⁰-1 = 1(9)_170<171> = 372939703851234256631_<21> · 1476778544474435499113_<22> · C129
C129 = P54 · P75
P54 = 435805161629542059835776832137316524513544223593929263_<54>
P75 = 833265940121934456634651862380154649875027665246097890955759336287836945791_<75>

Wed May 06 23:55:15 2009 Msieve v. 1.41 Wed May 06 23:55:15 2009 random seeds: f3d57740 5a083f78 Wed May 06 23:55:15 2009 factoring 363141597715231961840469669719391341355478061523847951174507517995879853212559878525994104711390336716937987367736368470819582033 (129 digits) Wed May 06 23:55:16 2009 searching for 15-digit factors Wed May 06 23:55:18 2009 commencing number field sieve (129-digit input) Wed May 06 23:55:18 2009 R0: -10000000000000000000000000000000000 Wed May 06 23:55:18 2009 R1: 1 Wed May 06 23:55:18 2009 A0: -1 Wed May 06 23:55:18 2009 A1: 0 Wed May 06 23:55:18 2009 A2: 0 Wed May 06 23:55:18 2009 A3: 0 Wed May 06 23:55:18 2009 A4: 0 Wed May 06 23:55:18 2009 A5: 2 Wed May 06 23:55:18 2009 skew 0.87, size 1.292301e-011, alpha 1.449076, combined = 3.697836e-010 Wed May 06 23:55:18 2009 Wed May 06 23:55:18 2009 commencing relation filtering Wed May 06 23:55:18 2009 commencing duplicate removal, pass 1 Wed May 06 23:56:41 2009 found 1638964 hash collisions in 11577617 relations Wed May 06 23:57:02 2009 added 368119 free relations Wed May 06 23:57:02 2009 commencing duplicate removal, pass 2 Wed May 06 23:57:21 2009 found 1606009 duplicates and 10339726 unique relations Wed May 06 23:57:21 2009 memory use: 65.3 MB Wed May 06 23:57:21 2009 reading rational ideals above 8323072 Wed May 06 23:57:21 2009 reading algebraic ideals above 8323072 Wed May 06 23:57:21 2009 commencing singleton removal, pass 1 Wed May 06 23:58:46 2009 relations with 0 large ideals: 322046 Wed May 06 23:58:46 2009 relations with 1 large ideals: 1627628 Wed May 06 23:58:46 2009 relations with 2 large ideals: 3355941 Wed May 06 23:58:46 2009 relations with 3 large ideals: 3166722 Wed May 06 23:58:46 2009 relations with 4 large ideals: 1327236 Wed May 06 23:58:46 2009 relations with 5 large ideals: 200079 Wed May 06 23:58:46 2009 relations with 6 large ideals: 340074 Wed May 06 23:58:46 2009 relations with 7+ large ideals: 0 Wed May 06 23:58:46 2009 10339726 relations and about 9650898 large ideals Wed May 06 23:58:46 2009 commencing singleton removal, pass 2 Thu May 07 00:00:11 2009 found 3518074 singletons Thu May 07 00:00:11 2009 current dataset: 6821652 relations and about 5201006 large ideals Thu May 07 00:00:11 2009 commencing singleton removal, pass 3 Thu May 07 00:01:08 2009 found 1186005 singletons Thu May 07 00:01:08 2009 current dataset: 5635647 relations and about 3937334 large ideals Thu May 07 00:01:08 2009 commencing singleton removal, pass 4 Thu May 07 00:01:56 2009 found 344484 singletons Thu May 07 00:01:56 2009 current dataset: 5291163 relations and about 3584584 large ideals Thu May 07 00:01:56 2009 commencing singleton removal, final pass Thu May 07 00:02:45 2009 memory use: 83.8 MB Thu May 07 00:02:45 2009 commencing in-memory singleton removal Thu May 07 00:02:45 2009 begin with 5291163 relations and 3793818 unique ideals Thu May 07 00:02:50 2009 reduce to 4676325 relations and 3166223 ideals in 14 passes Thu May 07 00:02:50 2009 max relations containing the same ideal: 30 Thu May 07 00:02:51 2009 reading rational ideals above 720000 Thu May 07 00:02:51 2009 reading algebraic ideals above 720000 Thu May 07 00:02:51 2009 commencing singleton removal, final pass Thu May 07 00:03:45 2009 keeping 3960255 ideals with weight <= 20, new excess is 329215 Thu May 07 00:03:49 2009 memory use: 128.4 MB Thu May 07 00:03:49 2009 commencing in-memory singleton removal Thu May 07 00:03:50 2009 begin with 4677019 relations and 3960255 unique ideals Thu May 07 00:03:55 2009 reduce to 4662695 relations and 3942575 ideals in 10 passes Thu May 07 00:03:55 2009 max relations containing the same ideal: 20 Thu May 07 00:03:58 2009 removing 962657 relations and 793542 ideals in 169115 cliques Thu May 07 00:03:58 2009 commencing in-memory singleton removal Thu May 07 00:03:58 2009 begin with 3700038 relations and 3942575 unique ideals Thu May 07 00:04:02 2009 reduce to 3580213 relations and 3023676 ideals in 8 passes Thu May 07 00:04:02 2009 max relations containing the same ideal: 20 Thu May 07 00:04:04 2009 removing 706590 relations and 537475 ideals in 169115 cliques Thu May 07 00:04:04 2009 commencing in-memory singleton removal Thu May 07 00:04:04 2009 begin with 2873623 relations and 3023676 unique ideals Thu May 07 00:04:06 2009 reduce to 2790515 relations and 2399228 ideals in 7 passes Thu May 07 00:04:06 2009 max relations containing the same ideal: 20 Thu May 07 00:04:08 2009 removing 62997 relations and 53600 ideals in 9397 cliques Thu May 07 00:04:08 2009 commencing in-memory singleton removal Thu May 07 00:04:08 2009 begin with 2727518 relations and 2399228 unique ideals Thu May 07 00:04:09 2009 reduce to 2726829 relations and 2344936 ideals in 5 passes Thu May 07 00:04:09 2009 max relations containing the same ideal: 20 Thu May 07 00:04:10 2009 relations with 0 large ideals: 9379 Thu May 07 00:04:10 2009 relations with 1 large ideals: 72170 Thu May 07 00:04:10 2009 relations with 2 large ideals: 332378 Thu May 07 00:04:10 2009 relations with 3 large ideals: 740524 Thu May 07 00:04:10 2009 relations with 4 large ideals: 848156 Thu May 07 00:04:10 2009 relations with 5 large ideals: 512541 Thu May 07 00:04:10 2009 relations with 6 large ideals: 180606 Thu May 07 00:04:10 2009 relations with 7+ large ideals: 31075 Thu May 07 00:04:10 2009 commencing 2-way merge Thu May 07 00:04:12 2009 reduce to 1798033 relation sets and 1416140 unique ideals Thu May 07 00:04:12 2009 commencing full merge Thu May 07 00:04:41 2009 memory use: 127.7 MB Thu May 07 00:04:41 2009 found 900031 cycles, need 848340 Thu May 07 00:04:41 2009 weight of 848340 cycles is about 59797514 (70.49/cycle) Thu May 07 00:04:41 2009 distribution of cycle lengths: Thu May 07 00:04:41 2009 1 relations: 56751 Thu May 07 00:04:41 2009 2 relations: 83118 Thu May 07 00:04:41 2009 3 relations: 96995 Thu May 07 00:04:41 2009 4 relations: 95528 Thu May 07 00:04:41 2009 5 relations: 90120 Thu May 07 00:04:41 2009 6 relations: 80315 Thu May 07 00:04:41 2009 7 relations: 70905 Thu May 07 00:04:41 2009 8 relations: 60666 Thu May 07 00:04:41 2009 9 relations: 51810 Thu May 07 00:04:41 2009 10+ relations: 162132 Thu May 07 00:04:41 2009 heaviest cycle: 18 relations Thu May 07 00:04:41 2009 commencing cycle optimization Thu May 07 00:04:43 2009 start with 5196529 relations Thu May 07 00:04:56 2009 pruned 170872 relations Thu May 07 00:04:56 2009 memory use: 128.9 MB Thu May 07 00:04:56 2009 distribution of cycle lengths: Thu May 07 00:04:56 2009 1 relations: 56751 Thu May 07 00:04:56 2009 2 relations: 85525 Thu May 07 00:04:56 2009 3 relations: 101683 Thu May 07 00:04:56 2009 4 relations: 99412 Thu May 07 00:04:56 2009 5 relations: 93679 Thu May 07 00:04:56 2009 6 relations: 82681 Thu May 07 00:04:56 2009 7 relations: 72480 Thu May 07 00:04:56 2009 8 relations: 61297 Thu May 07 00:04:56 2009 9 relations: 51549 Thu May 07 00:04:56 2009 10+ relations: 143283 Thu May 07 00:04:56 2009 heaviest cycle: 18 relations Thu May 07 00:04:58 2009 RelProcTime: 568 Thu May 07 00:04:58 2009 Thu May 07 00:04:58 2009 commencing linear algebra Thu May 07 00:04:58 2009 read 848340 cycles Thu May 07 00:05:00 2009 cycles contain 2518833 unique relations Thu May 07 00:05:56 2009 read 2518833 relations Thu May 07 00:05:59 2009 using 20 quadratic characters above 134214764 Thu May 07 00:06:12 2009 building initial matrix Thu May 07 00:06:44 2009 memory use: 275.6 MB Th