Since June 16, 2000

STUDIO KAMADA

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News and updates, December 2007

Dec 31, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(2·10¹⁶⁶+7)/9 = (2)₁₆₅3_<166> = 3² · 13 · 19 · 2203 · 92591638837_<11> · C148
C148 = P62 · P87
P62 = 10579117484643669985321526488483937482639067300717328050482541_<62>
P87 = 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651_<87>

Number: n N=4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191 ( 148 digits) SNFS difficulty: 166 digits. Divisors found: Mon Dec 31 10:05:46 2007 prp62 factor: 10579117484643669985321526488483937482639067300717328050482541 Mon Dec 31 10:05:46 2007 prp87 factor: 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651 Mon Dec 31 10:05:46 2007 elapsed time 01:19:50 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 48.46 hours. Scaled time: 63.48 units (timescale=1.310). Factorization parameters were as follows: name: KA_2_165_3 n: 4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191 skew: 0.81 deg: 5 c5: 20 c0: 7 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2200000) Primes: RFBsize:230209, AFBsize:229397, largePrimes:7279611 encountered Relations: rels:6773272, finalFF:518245 Max relations in full relation-set: 28 Initial matrix: 459672 x 518245 with sparse part having weight 38557490. Pruned matrix : 415223 x 417585 with weight 27293794. Total sieving time: 45.28 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 48.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹⁵⁴-9 = 6(9)₁₅₃1_<155> = 24187568437147_<14> · 357505542381274647193_<21> · C121
C121 = P35 · P86
P35 = 87307807817705591131142443529365687_<35>
P86 = 92719261960991305708767306625668063796197431975684064005420378748486361040936361668683_<86>
7·10¹⁶⁵-9 = 6(9)₁₆₄1_<166> = 449 · 96293 · 193732283 · C150
C150 = P60 · P91
P60 = 119720935477183205712026361015748167111027951799849560997421_<60>
P91 = 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341_<91>

Number: n N=835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561 ( 150 digits) SNFS difficulty: 165 digits. Divisors found: Mon Dec 31 23:17:09 2007 prp60 factor: 119720935477183205712026361015748167111027951799849560997421 Mon Dec 31 23:17:09 2007 prp91 factor: 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341 Mon Dec 31 23:17:09 2007 elapsed time 02:16:22 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 58.35 hours. Scaled time: 102.75 units (timescale=1.761). Factorization parameters were as follows: name: KA_6_9_164_1 n: 835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561 type: snfs skew: 1.05 deg: 5 c5: 7 c0: -9 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2800001) Primes: RFBsize:230209, AFBsize:230717, largePrimes:7456900 encountered Relations: rels:6921697, finalFF:489538 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 58.10 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 58.35 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(7·10¹⁶⁴-61)/9 = (7)₁₆₃1_<164> = 67 · 16943 · 608743 · 4855817 · 723493411 · 103466618887166809_<18> · C120
C120 = P39 · P40 · P43
P39 = 200987859740178940829671987628842189511_<39>
P40 = 1524315768672965057529391990531835488823_<40>
P43 = 1010681974438265260089808346426272470700763_<43>

Tue Jan 01 00:33:37 2008 Tue Jan 01 00:33:37 2008 Tue Jan 01 00:33:37 2008 Msieve v. 1.32 Tue Jan 01 00:33:37 2008 random seeds: 670f8060 b722816b Tue Jan 01 00:33:37 2008 factoring 203134806920325175654885525513483664774580080235041609363980893235812401418296893 (81 digits) Tue Jan 01 00:33:37 2008 searching for 15-digit factors Tue Jan 01 00:33:38 2008 commencing quadratic sieve (80-digit input) Tue Jan 01 00:33:38 2008 using multiplier of 5 Tue Jan 01 00:33:38 2008 using 64kb Opteron sieve core Tue Jan 01 00:33:38 2008 sieve interval: 6 blocks of size 65536 Tue Jan 01 00:33:38 2008 processing polynomials in batches of 17 Tue Jan 01 00:33:38 2008 using a sieve bound of 1305691 (50294 primes) Tue Jan 01 00:33:38 2008 using large prime bound of 129263409 (26 bits) Tue Jan 01 00:33:38 2008 using trial factoring cutoff of 27 bits Tue Jan 01 00:33:38 2008 polynomial 'A' values have 10 factors Tue Jan 01 00:51:33 2008 50454 relations (25765 full + 24689 combined from 273397 partial), need 50390 Tue Jan 01 00:51:34 2008 begin with 299162 relations Tue Jan 01 00:51:34 2008 reduce to 72049 relations in 2 passes Tue Jan 01 00:51:34 2008 attempting to read 72049 relations Tue Jan 01 00:51:35 2008 recovered 72049 relations Tue Jan 01 00:51:35 2008 recovered 62785 polynomials Tue Jan 01 00:51:35 2008 attempting to build 50454 cycles Tue Jan 01 00:51:35 2008 found 50454 cycles in 1 passes Tue Jan 01 00:51:35 2008 distribution of cycle lengths: Tue Jan 01 00:51:35 2008 length 1 : 25765 Tue Jan 01 00:51:35 2008 length 2 : 24689 Tue Jan 01 00:51:35 2008 largest cycle: 2 relations Tue Jan 01 00:51:35 2008 matrix is 50294 x 50454 with weight 1538986 (avg 30.50/col) Tue Jan 01 00:51:35 2008 filtering completed in 4 passes Tue Jan 01 00:51:35 2008 matrix is 42992 x 43056 with weight 1286275 (avg 29.87/col) Tue Jan 01 00:51:35 2008 saving the first 48 matrix rows for later Tue Jan 01 00:51:35 2008 matrix is 42944 x 43056 with weight 1002106 (avg 23.27/col) Tue Jan 01 00:51:35 2008 matrix includes 64 packed rows Tue Jan 01 00:51:35 2008 commencing Lanczos iteration Tue Jan 01 00:52:18 2008 lanczos halted after 680 iterations (dim = 42920) Tue Jan 01 00:52:18 2008 recovered 6 nontrivial dependencies Tue Jan 01 00:52:18 2008 prp39 factor: 200987859740178940829671987628842189511 Tue Jan 01 00:52:18 2008 prp43 factor: 1010681974438265260089808346426272470700763 Tue Jan 01 00:52:18 2008 elapsed time 00:18:41

Dec 30, 2007 (2nd)

By Sinkiti Sibata / PFGW
(2·10²⁴⁴²+7)/9 is prime.

Dec 30, 2007

By Robert Backstrom / GGNFS, Msieve
(28·10¹⁶³+17)/9 = 3(1)₁₆₂3_<164> = 3 · 11 · 113 · 5227723 · 5474506657_<10> · C144
C144 = P54 · P90
P54 = 568254104215421080733918790780653788490645701320935561_<54>
P90 = 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507_<90>

Number: n N=291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427 ( 144 digits) SNFS difficulty: 164 digits. Divisors found: Sun Dec 30 22:22:57 2007 prp54 factor: 568254104215421080733918790780653788490645701320935561 Sun Dec 30 22:22:57 2007 prp90 factor: 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507 Sun Dec 30 22:22:57 2007 elapsed time 00:55:31 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.78 hours. Scaled time: 54.81 units (timescale=1.532). Factorization parameters were as follows: name: KA_3_1_162_3 n: 291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427 skew: 0.45 deg: 5 c5: 875 c0: 17 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2600000) Primes: RFBsize:216816, AFBsize:216531, largePrimes:7351213 encountered Relations: rels:6806772, finalFF:496921 Max relations in full relation-set: 28 Initial matrix: 433413 x 496921 with sparse part having weight 48938966. Pruned matrix : Total sieving time: 35.60 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 35.78 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(89·10¹⁶¹+1)/9 = 9(8)₁₆₀9_<162> = 11 · 151 · 54497 · 4734857424467_<13> · 29333719355391524558753_<23> · C119
C119 = P50 · P70
P50 = 24068764486818214538179925119843116225195355366201_<50>
P70 = 3267965275130364758731306727795381662655553549388276194815369559709367_<70>

Number: n N=78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767 ( 119 digits) SNFS difficulty: 162 digits. Divisors found: Sun Dec 30 22:54:11 2007 prp50 factor: 24068764486818214538179925119843116225195355366201 Sun Dec 30 22:54:11 2007 prp70 factor: 3267965275130364758731306727795381662655553549388276194815369559709367 Sun Dec 30 22:54:11 2007 elapsed time 01:13:42 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 37.56 hours. Scaled time: 31.47 units (timescale=0.838). Factorization parameters were as follows: name: KA_9_8_160_9 n: 78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767 type: snfs deg: 5 c5: 890 c0: 1 skew: 0.22 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3600001) Primes: RFBsize:216816, AFBsize:217061, largePrimes:5646354 encountered Relations: rels:5529662, finalFF:441875 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 37.45 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 37.56 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Dec 29, 2007 (2nd)

By Robert Backstrom / GMP-ECM
2·10¹⁶³+3 = 2(0)₁₆₂3_<164> = 166140237444137244767_<21> · C144
C144 = P39 · P105
P39 = 190635692847477990579123632346869310511_<39>
P105 = 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619_<105>
7·10¹⁵³-9 = 6(9)₁₅₂1_<154> = 137945979054044323691_<21> · C134
C134 = P33 · P101
P33 = 772167558584103691869638283989203_<33>
P101 = 65716956589780721844302884925214520835046088468765165698360498247128407329527151604691722545317100967_<101>

Dec 29, 2007

By Jo Yeong Uk / GGNFS
7·10¹⁴⁸-9 = 6(9)₁₄₇1_<149> = 7354479179_<10> · 18371504286793171_<17> · C123
C123 = P55 · P69
P55 = 2814258676699625279171724231993155814622006129842908123_<55>
P69 = 184093046599172102452699913165893938014185229449403497478166109476613_<69>

Number: 69991_148 N=518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399 ( 123 digits) SNFS difficulty: 150 digits. Divisors found: r1=2814258676699625279171724231993155814622006129842908123 (pp55) r2=184093046599172102452699913165893938014185229449403497478166109476613 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.54 hours. Scaled time: 33.21 units (timescale=2.137). Factorization parameters were as follows: n: 518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399 m: 1000000000000000000000000000000 c5: 7 c0: -900 skew: 2.64 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:175703, largePrimes:5573819 encountered Relations: rels:5511681, finalFF:495649 Max relations in full relation-set: 28 Initial matrix: 352073 x 495649 with sparse part having weight 44562981. Pruned matrix : 293821 x 295645 with weight 24414844. Total sieving time: 15.02 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.40 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 15.54 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (4th)

By Sinkiti Sibata / GGNFS
3·10¹⁷¹+1 = 3(0)₁₇₀1_<172> = 59 · 2421821 · 1600388452377973_<16> · 19226964394318121967711782431_<29> · C120
C120 = P42 · P79
P42 = 454231567465961238949597490091615349190531_<42>
P79 = 1502151578223577638654775137097332901436078950967469661170957656557872845681903_<79>

Number: 30001_171 N=682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493 ( 120 digits) Divisors found: r1=454231567465961238949597490091615349190531 (pp42) r2=1502151578223577638654775137097332901436078950967469661170957656557872845681903 (pp79) Version: GGNFS-0.77.1-20060722-nocona Total time: 72.45 hours. Scaled time: 143.38 units (timescale=1.979). Factorization parameters were as follows: name: 30001_171 n: 682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493 skew: 44071.04 # norm 1.16e+16 c5: 49080 c4: -8193826874 c3: -490521821772937 c2: 13679562189223828075 c1: 268407340291989159886011 c0: -3575626527912292763955712170 # alpha -5.23 Y1: 1376995663549 Y0: -106811371197497656583221 # Murphy_E 2.89e-10 # M 516601066594921290271387127147345628955044795772215321251305996854853784465683210678704718808492261730386730080006420124 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4350001) Primes: RFBsize:315948, AFBsize:316211, largePrimes:7704182 encountered Relations: rels:7780725, finalFF:757685 Max relations in full relation-set: 32 Initial matrix: 632244 x 757685 with sparse part having weight 71595438. Pruned matrix : 531677 x 534902 with weight 46827802. Total sieving time: 67.50 hours. Total relation processing time: 0.43 hours. Matrix solve time: 4.05 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 72.45 hours. --------- CPU info (if available) ----------

Dec 28, 2007 (3rd)

By Jo Yeong Uk / GGNFS
7·10¹⁴⁰-9 = 6(9)₁₃₉1_<141> = 26003 · 49967046113187701_<17> · C120
C120 = P49 · P72
P49 = 3072384756632832193294930209979933326902287322161_<49>
P72 = 175353850256855514724412620180648233024414774451978568104314670271200777_<72>

Number: 70009_140 N=538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097 ( 120 digits) SNFS difficulty: 140 digits. Divisors found: r1=3072384756632832193294930209979933326902287322161 (pp49) r2=175353850256855514724412620180648233024414774451978568104314670271200777 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.12 hours. Scaled time: 13.11 units (timescale=2.144). Factorization parameters were as follows: n: 538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097 m: 10000000000000000000000000000 c5: 7 c0: -9 skew: 1.05 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368951 encountered Relations: rels:3483950, finalFF:405792 Max relations in full relation-set: 28 Initial matrix: 228213 x 405792 with sparse part having weight 35387880. Pruned matrix : 168806 x 170011 with weight 13391873. Total sieving time: 5.95 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.12 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁴⁴-9 = 6(9)₁₄₃1_<145> = 1487 · 3084617 · 6753139867_<10> · C126
C126 = P55 · P72
P55 = 2066420873807475272508154570496764559275489805725499291_<55>
P72 = 109360704402145490620976185805347880615820804660378980898198273592328057_<72>

Number: 69991_144 N=225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587 ( 126 digits) SNFS difficulty: 145 digits. Divisors found: r1=2066420873807475272508154570496764559275489805725499291 (pp55) r2=109360704402145490620976185805347880615820804660378980898198273592328057 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.14 hours. Scaled time: 21.75 units (timescale=2.144). Factorization parameters were as follows: n: 225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587 m: 100000000000000000000000000000 c5: 7 c0: -90 skew: 1.67 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1450001) Primes: RFBsize:114155, AFBsize:114352, largePrimes:3482197 encountered Relations: rels:3539168, finalFF:329576 Max relations in full relation-set: 28 Initial matrix: 228573 x 329576 with sparse part having weight 32251907. Pruned matrix : 200812 x 202018 with weight 16980012. Total sieving time: 9.89 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.17 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 10.14 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
7·10¹⁸⁶-9 = 6(9)₁₈₅1_<187> = 1882873212211_<13> · 5833979226117373_<16> · 47533639674475314086029_<23> · 22494947546032604356359491_<26> · C111
C111 = P43 · P69
P43 = 2515472027805282686708792675704535850836383_<43>
P69 = 236922626264959098658721156310440198919184175106191358028227502394681_<69>

Number: n N=595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823 ( 111 digits) Divisors found: r1=2515472027805282686708792675704535850836383 (pp43) r2=236922626264959098658721156310440198919184175106191358028227502394681 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.07 hours. Scaled time: 33.44 units (timescale=1.753). Factorization parameters were as follows: name: KA_6_9_185_1 n: 595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823 skew: 7691.60 # norm 7.39e+14 c5: 65280 c4: -3707517143 c3: -59981266406565 c2: 195444948138712791 c1: 464656384627185252258 c0: -666305598531814435117600 # alpha -4.72 Y1: 299854219969 Y0: -1556288568485250579843 # Murphy_E 8.93e-10 # M 261347015577692975215738963466108609772390237867217698520093975466862424241959027489401092781747038850578899133 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 100000) Primes: RFBsize:230209, AFBsize:229965, largePrimes:7449706 encountered Relations: rels:7280948, finalFF:562779 Max relations in full relation-set: 28 Initial matrix: 460254 x 562779 with sparse part having weight 47426767. Pruned matrix : 375082 x 377447 with weight 27995113. Total sieving time: 16.82 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.45 hours. Total square root time: 0.65 hours, sqrts: 4. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.07 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹⁵⁸-9 = 6(9)₁₅₇1_<159> = 665507 · 4787893769_<10> · C144
C144 = P34 · P110
P34 = 4551229532797823713440523924237357_<34>
P110 = 48269429654485286004700435874371392955763120608188765913835335149678303496468383067863156974558912669025897961_<110>
5·10¹⁶⁷+3 = 5(0)₁₆₆3_<168> = 7 · 773 · 8329 · C161
C161 = P68 · P93
P68 = 66986389608208370945649030468786635518218514529828739674619854324867_<68>
P93 = 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811_<93>

Number: n N=11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137 ( 161 digits) SNFS difficulty: 167 digits. Divisors found: Fri Dec 28 08:58:01 2007 prp68 factor: 66986389608208370945649030468786635518218514529828739674619854324867 Fri Dec 28 08:58:01 2007 prp93 factor: 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811 Fri Dec 28 08:58:01 2007 elapsed time 01:10:29 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 46.34 hours. Scaled time: 84.62 units (timescale=1.826). Factorization parameters were as follows: name: KA_5_0_166_3 n: 11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137 skew: 0.36 deg: 5 c5: 500 c0: 3 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200000) Primes: RFBsize:250150, AFBsize:249916, largePrimes:7647488 encountered Relations: rels:7156043, finalFF:585019 Max relations in full relation-set: 28 Initial matrix: 500132 x 585019 with sparse part having weight 52070590. Pruned matrix : 452893 x 455457 with weight 34748113. Total sieving time: 46.16 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 46.34 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Dec 28, 2007

By Sinkiti Sibata / PFGW
7·10¹²⁷⁵⁵-9 and 7·10¹⁵¹⁴²-9 are PRPs.

Dec 27, 2007 (5th)

By Yousuke Koide
(10¹⁸⁰⁹-1)/9 is divisible by 23016857713231589991096649713043507_<35>
(10¹⁸⁶³-1)/9 is divisible by 7506789884668978259450285467_<28>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 27, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM
7·10¹³⁷-9 = 6(9)₁₃₆1_<138> = 9041 · 162129560783_<12> · C123
C123 = P50 · P73
P50 = 63195768153342995547599618615921084920365446753767_<50>
P73 = 7556685842419476053247753995520570438772601000514461987314342496480958991_<73>

Number: 69991_137 N=477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097 ( 123 digits) SNFS difficulty: 137 digits. Divisors found: r1=63195768153342995547599618615921084920365446753767 (pp50) r2=7556685842419476053247753995520570438772601000514461987314342496480958991 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.07 hours. Scaled time: 8.67 units (timescale=2.130). Factorization parameters were as follows: n: 477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097 m: 1000000000000000000000000000 c5: 700 c0: -9 skew: 0.42 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1450001) Primes: RFBsize:107126, AFBsize:107093, largePrimes:2316731 encountered Relations: rels:2429777, finalFF:264060 Max relations in full relation-set: 28 Initial matrix: 214287 x 264060 with sparse part having weight 22014166. Pruned matrix : 198204 x 199339 with weight 13643617. Total sieving time: 3.87 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 4.07 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁶²-9 = 6(9)₁₆₁1_<163> = 859 · 118247 · 2662639391_<10> · 68628329971_<11> · C135
C135 = P30 · P105
P30 = 436977788659416077831566216483_<30>
P105 = 863057237779628902143622988929371538585971609219344275040457451654589439284920068001169478963439353329509_<105>

Dec 27, 2007 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
5·10¹⁷¹-9 = 4(9)₁₇₀1_<172> = 7 · 41 · C170
C170 = P43 · P128
P43 = 1363684689367687199660001585916252959225073_<43>
P128 = 12775389298778802140820274185385735600606854567622114532762344954306460995067145385939039085787137146377153359945100703455866041_<128>
7·10¹⁴³-9 = 6(9)₁₄₂1_<144> = 97 · 317 · 571 · C137
C137 = P68 · P70
P68 = 11669963674208858774803484401760836297661604636382205067928038771673_<68>
P70 = 3416342715437805134104596866257027736379971208960481691857755728114273_<70>

Number: n N=39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729 ( 137 digits) SNFS difficulty: 143 digits. Divisors found: Thu Dec 27 16:03:21 2007 prp68 factor: 11669963674208858774803484401760836297661604636382205067928038771673 Thu Dec 27 16:03:21 2007 prp70 factor: 3416342715437805134104596866257027736379971208960481691857755728114273 Thu Dec 27 16:03:21 2007 elapsed time 00:58:19 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 10.12 hours. Scaled time: 13.24 units (timescale=1.309). Factorization parameters were as follows: name: KA_6_9_142_1 n: 39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729 skew: 0.26 deg: 5 c5: 7000 c0: -9 m: 10000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1100001) Primes: RFBsize:203362, AFBsize:202857, largePrimes:6879960 encountered Relations: rels:6390626, finalFF:531267 Max relations in full relation-set: 28 Initial matrix: 406287 x 531267 with sparse part having weight 31643740. Pruned matrix : Total sieving time: 9.91 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 10.12 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹⁹⁴-9 = 6(9)₁₉₃1_<195> = 59 · 503 · 19009 · 4546319117_<10> · 3201890183553739545421_<22> · 3663534177803835316717_<22> · 5453825411908180414535101_<25> · C109
C109 = P47 · P62
P47 = 52063286361231377503035962252713421659616793211_<47>
P62 = 81944416344344076297954674797070896167668217005498046483209993_<62>

Number: n N=4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523 ( 109 digits) Divisors found: Thu Dec 27 21:14:40 2007 prp47 factor: 52063286361231377503035962252713421659616793211 Thu Dec 27 21:14:40 2007 prp62 factor: 81944416344344076297954674797070896167668217005498046483209993 Thu Dec 27 21:14:40 2007 elapsed time 01:21:04 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 15.97 hours. Scaled time: 28.00 units (timescale=1.753). Factorization parameters were as follows: name: KA_6_9_193_1 n: 4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523 skew: 20303.21 # norm 3.02e+15 c5: 64260 c4: -5524240892 c3: 33370301956429 c2: 2960552805759545129 c1: 13268125763144698600299 c0: -427943730192357035630844 # alpha -6.40 Y1: 410046852743 Y0: -581336125346552761433 # Murphy_E 1.18e-09 # M 835049287715849898352208609708011149328452835128639575533350171456753898162996679714302558410477726301170271 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1700000) Primes: RFBsize:230209, AFBsize:229921, largePrimes:6992043 encountered Relations: rels:6742934, finalFF:579789 Max relations in full relation-set: 28 Initial matrix: 460216 x 579789 with sparse part having weight 39572835. Pruned matrix : 350884 x 353249 with weight 18553288. Total sieving time: 15.64 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: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 15.97 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹⁰⁸-9 = 6(9)₁₀₇1_<109> = 404321 · 378807857 · C95
C95 = P46 · P50
P46 = 2663967441313171836581746263544242756268412123_<46>
P50 = 17156308633252668896929507566790813539577265672261_<50>

Number: n N=45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103 ( 95 digits) Divisors found: r1=2663967441313171836581746263544242756268412123 (pp46) r2=17156308633252668896929507566790813539577265672261 (pp50) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.81 hours. Scaled time: 8.43 units (timescale=1.754). Factorization parameters were as follows: name: KA_6_9_107_1 n: 45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103 m: 5492465041505502450157 deg: 4 c4: 50220792 c3: 473490998762 c2: -150320131923816106 c1: -1840155014132418213 c0: 240325391527681110358680 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.908 # E(F1,F2) = 4.085225e-05 # GGNFS version 0.77.1-20050930-k8 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198729570. # 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 special-q in [100000, 100000) Primes: RFBsize:92938, AFBsize:92993, largePrimes:1857627 encountered Relations: rels:1908164, finalFF:212612 Max relations in full relation-set: 28 Initial matrix: 186005 x 212612 with sparse part having weight 16282353. Pruned matrix : 174218 x 175212 with weight 11293718. Total sieving time: 4.41 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.30 hours. Total square root time: 0.04 hours, sqrts: 14. 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: 4.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹⁴⁵-9 = 6(9)₁₄₄1_<146> = 94261 · C141
C141 = P34 · P108
P34 = 1021695068102849396044532089064863_<34>
P108 = 726849841772289840962937682508573633040889067399121266108989206433699098743911136797514039693842951036128037_<108>

Dec 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS
7·10¹¹³-9 = 6(9)₁₁₂1_<114> = 491 · 2423 · 4003873 · C102
C102 = P48 · P54
P48 = 184432465107840005841929350652158018855881137453_<48>
P54 = 796792925041443202307060294296189274485989498333919823_<54>

Number: 69991_113 N=146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819 ( 102 digits) SNFS difficulty: 113 digits. Divisors found: r1=184432465107840005841929350652158018855881137453 (pp48) r2=796792925041443202307060294296189274485989498333919823 (pp54) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.40 hours. Scaled time: 1.62 units (timescale=0.675). Factorization parameters were as follows: name: 69991_113 n: 146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819 m: 10000000000000000000000 c5: 7000 c0: -9 skew: 0.26 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63823, largePrimes:2223893 encountered Relations: rels:2457553, finalFF:359535 Max relations in full relation-set: 28 Initial matrix: 112989 x 359535 with sparse part having weight 31384555. Pruned matrix : 71414 x 72042 with weight 5203701. Total sieving time: 2.19 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.40 hours. --------- CPU info (if available) ----------

7·10¹³⁵-9 = 6(9)₁₃₄1_<136> = 3673 · 255019 · 84498497 · 15088353311_<11> · C109
C109 = P37 · P73
P37 = 2619090469168430611738435623980583053_<37>
P73 = 2238016293251830424874207565385593578321653128229251831899397482529153343_<73>

Number: 69991_135 N=5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179 ( 109 digits) SNFS difficulty: 135 digits. Divisors found: r1=2619090469168430611738435623980583053 (pp37) r2=2238016293251830424874207565385593578321653128229251831899397482529153343 (pp73) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.83 hours. Scaled time: 13.67 units (timescale=2.003). Factorization parameters were as follows: name: 69991_135 n: 5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179 m: 1000000000000000000000000000 c5: 7 c0: -9 skew: 1.05 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1225001) Primes: RFBsize:78498, AFBsize:63908, largePrimes:1579365 encountered Relations: rels:1604122, finalFF:195607 Max relations in full relation-set: 28 Initial matrix: 142472 x 195607 with sparse part having weight 16386599. Pruned matrix : 126424 x 127200 with weight 8919279. Total sieving time: 6.60 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.11 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.83 hours. --------- CPU info (if available) ----------

7·10¹⁴⁷-9 = 6(9)₁₄₆1_<148> = 44253346650419_<14> · 640263926981563_<15> · 2384930862846177191492797_<25> · C96
C96 = P36 · P60
P36 = 345533806013666402094028972113839143_<36>
P60 = 299796493353162488095487968396822078060268288441471385866693_<60>

Number: 69991_147 N=103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099 ( 96 digits) Divisors found: r1=345533806013666402094028972113839143 (pp36) r2=299796493353162488095487968396822078060268288441471385866693 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 11.00 hours. Scaled time: 7.42 units (timescale=0.675). Factorization parameters were as follows: name: 69991_147 n: 103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099 m: 7455843658268344282957 deg: 4 c4: 33522000 c3: 140814788 c2: 77276617925738599 c1: 69424401729227304416 c0: 2357246899800669557952 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.016 # E(F1,F2) = 2.812171e-05 # GGNFS version 0.77.1-20060513-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198709841. # 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, 1500001) Primes: RFBsize:92938, AFBsize:92936, largePrimes:1911524 encountered Relations: rels:2002935, finalFF:233843 Max relations in full relation-set: 28 Initial matrix: 185950 x 233843 with sparse part having weight 21496159. Pruned matrix : 166071 x 167064 with weight 13108251. Polynomial selection time: 0.17 hours. Total sieving time: 9.92 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.72 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 11.00 hours. --------- CPU info (if available) ----------

Dec 27, 2007

By Sinkiti Sibata / GGNFS
7·10¹³³-9 = 6(9)₁₃₂1_<134> = 449 · 1493 · 90917 · 94389114492319_<14> · C110
C110 = P44 · P66
P44 = 85173022756831337810382828011673697322037311_<44>
P66 = 142864005459473961587757841830261127716190760624346731496837517471_<66>

Number: 69991_133 N=12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481 ( 110 digits) SNFS difficulty: 133 digits. Divisors found: r1=85173022756831337810382828011673697322037311 (pp44) r2=142864005459473961587757841830261127716190760624346731496837517471 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 8.35 hours. Scaled time: 16.72 units (timescale=2.003). Factorization parameters were as follows: name: 69991_133 n: 12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481 m: 100000000000000000000000000 c5: 7000 c0: -9 skew: 0.26 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1375001) Primes: RFBsize:78498, AFBsize:63823, largePrimes:1568311 encountered Relations: rels:1565951, finalFF:168189 Max relations in full relation-set: 28 Initial matrix: 142389 x 168189 with sparse part having weight 15197800. Pruned matrix : 134600 x 135375 with weight 10638770. Total sieving time: 8.08 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.15 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 8.35 hours. --------- CPU info (if available) ----------

Dec 26, 2007 (6th)

By Sinkiti Sibata / PRIMO
(2·10²⁹⁷⁸-17)/3 is prime.

Dec 26, 2007 (5th)

By Sinkiti Sibata / GGNFS
7·10¹¹⁸-9 = 6(9)₁₁₇1_<119> = 29 · 281 · 479 · 564899 · C107
C107 = P34 · P74
P34 = 1984136958064167375045366373528421_<34>
P74 = 15999844291278446970836451631567805232288393575182670206207520554418064299_<74>

Number: 69991_118 N=31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879 ( 107 digits) SNFS difficulty: 118 digits. Divisors found: r1=1984136958064167375045366373528421 (pp34) r2=15999844291278446970836451631567805232288393575182670206207520554418064299 (pp74) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.24 hours. Scaled time: 4.45 units (timescale=1.991). Factorization parameters were as follows: name: 69991_118 n: 31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879 m: 100000000000000000000000 c5: 7000 c0: -9 skew: 0.26 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63823, largePrimes:2167506 encountered Relations: rels:2281489, finalFF:242097 Max relations in full relation-set: 28 Initial matrix: 112989 x 242097 with sparse part having weight 22238741. Pruned matrix : 87145 x 87773 with weight 5534433. Total sieving time: 2.10 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.24 hours. --------- CPU info (if available) ----------

7·10¹²²-9 = 6(9)₁₂₁1_<123> = 83 · 13523 · 244861 · 1071691642724939_<16> · C97
C97 = P44 · P53
P44 = 82895830946665960950649287503567133316049651_<44>
P53 = 28669805558837951631417683899953649248910278323675131_<53>

Number: 69991_122 N=2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281 ( 97 digits) SNFS difficulty: 122 digits. Divisors found: r1=82895830946665960950649287503567133316049651 (pp44) r2=28669805558837951631417683899953649248910278323675131 (pp53) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.38 hours. Scaled time: 6.77 units (timescale=2.003). Factorization parameters were as follows: name: 69991_122 n: 2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281 m: 1000000000000000000000000 c5: 700 c0: -9 skew: 0.42 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63803, largePrimes:2446192 encountered Relations: rels:2891407, finalFF:532620 Max relations in full relation-set: 28 Initial matrix: 112969 x 532620 with sparse part having weight 52760048. Pruned matrix : 76482 x 77110 with weight 9438717. Total sieving time: 3.23 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.38 hours. --------- CPU info (if available) ----------

7·10¹³²-9 = 6(9)₁₃₁1_<133> = 1292567 · 190646486287_<12> · C116
C116 = P41 · P76
P41 = 10653299394346279999189253853948866948741_<41>
P76 = 2666441366915221621544897168193843156735547511317187784920639757035112567619_<76>

Number: 69991_132 N=28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679 ( 116 digits) SNFS difficulty: 132 digits. Divisors found: r1=10653299394346279999189253853948866948741 (pp41) r2=2666441366915221621544897168193843156735547511317187784920639757035112567619 (pp76) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.77 hours. Scaled time: 11.49 units (timescale=1.991). Factorization parameters were as follows: name: 69991_132 n: 28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679 m: 100000000000000000000000000 c5: 700 c0: -9 skew: 0.42 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1150001) Primes: RFBsize:63951, AFBsize:63803, largePrimes:1538473 encountered Relations: rels:1545151, finalFF:170046 Max relations in full relation-set: 28 Initial matrix: 127822 x 170046 with sparse part having weight 14925657. Pruned matrix : 117194 x 117897 with weight 8533990. Total sieving time: 5.57 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.77 hours. --------- CPU info (if available) ----------

Dec 26, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM
7·10¹¹⁷-9 = 6(9)₁₁₆1_<118> = C118
C118 = P48 · P70
P48 = 965127703405741647531200158987421082342396773977_<48>
P70 = 7252926193392239386243000349720048960099140101219877063658000208088783_<70>

Number: 69991_117 N=6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 118 digits) SNFS difficulty: 117 digits. Divisors found: r1=965127703405741647531200158987421082342396773977 (pp48) r2=7252926193392239386243000349720048960099140101219877063658000208088783 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.05 hours. Scaled time: 2.25 units (timescale=2.145). Factorization parameters were as follows: n: 6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 100000000000000000000000 c5: 700 c0: -9 skew: 0.42 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [300000, 450001) Primes: RFBsize:49098, AFBsize:49186, largePrimes:1878131 encountered Relations: rels:1929377, finalFF:194599 Max relations in full relation-set: 28 Initial matrix: 98352 x 194599 with sparse part having weight 16935639. Pruned matrix : 78199 x 78754 with weight 4525630. Total sieving time: 1.00 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 1.05 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁵²-9 = 6(9)₁₅₁1_<153> = 642738965504016239_<18> · C136
C136 = P32 · P104
P32 = 12499425996572633795685838286539_<32>
P104 = 87131128901653143200613872829832683606052695848751370614553206443217691319643034696885938619060585421771_<104>

Dec 26, 2007 (3rd)

By matsui / GGNFS
2·10¹⁶⁷+9 = 2(0)₁₆₆9_<168> = 47 · 184481867 · 10008810089_<11> · 118729587401_<12> · 10440234088181_<14> · C124
C124 = P61 · P63
P61 = 6290280740566369228935563961231140837620944228695383054749943_<61>
P63 = 295567569227359507343672924451640185453395509237894904088703543_<63>

N=1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049 ( 124 digits) SNFS difficulty: 167 digits. Divisors found: r1=6290280740566369228935563961231140837620944228695383054749943 (pp61) r2=295567569227359507343672924451640185453395509237894904088703543 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 127.80 hours. Scaled time: 166.65 units (timescale=1.304). Factorization parameters were as follows: n: 1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049 m: 1000000000000000000000000000000000 c5: 200 c0: 9 skew: 0.54 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 5450001) Primes: RFBsize:380800, AFBsize:380082, largePrimes:5892464 encountered Relations: rels:6135246, finalFF:894339 Max relations in full relation-set: 28 Initial matrix: 760947 x 894339 with sparse part having weight 44957251. Pruned matrix : 648054 x 651922 with weight 30819584. Total sieving time: 114.05 hours. Total relation processing time: 0.20 hours. Matrix solve time: 13.26 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 127.80 hours.

Dec 26, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(22·10¹⁶⁶-1)/3 = 7(3)_166<167> = 13 · 2501184977_<10> · C157
C157 = P47 · P111
P47 = 20970006021949093438264942952242363969867903567_<47>
P111 = 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399_<111>

Number: n N=2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233 ( 157 digits) SNFS difficulty: 167 digits. Divisors found: Wed Dec 26 05:26:18 2007 prp47 factor: 20970006021949093438264942952242363969867903567 Wed Dec 26 05:26:18 2007 prp111 factor: 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399 Wed Dec 26 05:26:18 2007 elapsed time 02:18:47 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 78.83 hours. Scaled time: 138.12 units (timescale=1.752). Factorization parameters were as follows: name: KA_7_3_166 n: 2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233 type: snfs skew: 0.34 deg: 5 c5: 220 c0: -1 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3500001) Primes: RFBsize:230209, AFBsize:230048, largePrimes:7684784 encountered Relations: rels:7152361, finalFF:475660 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 78.54 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000 total time: 78.83 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹²⁰-9 = 6(9)₁₁₉1_<121> = 197 · 419 · C116
C116 = P52 · P65
P52 = 1323129079639263647678527821934298050401138159281717_<52>
P65 = 64093734415499366088944419295581630353010019359658087508532919861_<65>

Number: n N=84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337 ( 116 digits) SNFS difficulty: 120 digits. Divisors found: r1=1323129079639263647678527821934298050401138159281717 (pp52) r2=64093734415499366088944419295581630353010019359658087508532919861 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.47 hours. Scaled time: 2.59 units (timescale=1.755). Factorization parameters were as follows: name: KA_6_9_119_1 n: 84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337 type: snfs skew: 1.05 deg: 5 c5: 7 c0: -9 m: 1000000000000000000000000 rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 220001) Primes: RFBsize:78498, AFBsize:78361, largePrimes:4117883 encountered Relations: rels:3508482, finalFF:209284 Max relations in full relation-set: 28 Initial matrix: 156925 x 209284 with sparse part having weight 9419779. Pruned matrix : 113353 x 114201 with weight 3874739. Total sieving time: 1.28 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.10 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000 total time: 1.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(8·10¹⁶⁶-17)/9 = (8)₁₆₅7_<166> = 4083907 · 43094378617_<11> · C149
C149 = P41 · P51 · P58
P41 = 38584081030692973979026508694832853174717_<41>
P51 = 418114217260780904751406897239535819468897448269121_<51>
P58 = 3130746579328069205359019081831876161205414051790095798089_<58>

Number: n N=1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769 ( 109 digits) Divisors found: Thu Dec 27 01:08:55 2007 prp51 factor: 418114217260780904751406897239535819468897448269121 Thu Dec 27 01:08:55 2007 prp58 factor: 3130746579328069205359019081831876161205414051790095798089 Thu Dec 27 01:08:55 2007 elapsed time 00:56:09 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 14.81 hours. Scaled time: 19.34 units (timescale=1.306). Factorization parameters were as follows: name: KA_8_165_7 n: 1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769 skew: 17293.45 # norm 1.67e+15 c5: 69840 c4: 7463998242 c3: -78994172254267 c2: -2236017190191479429 c1: 14571241816633004474387 c0: 2943605098409076728592987 # alpha -6.80 Y1: 379170613327 Y0: -451398307899860421580 # Murphy_E 1.27e-09 # M 913262407536112418797141648337235351640361187128809490900940893449426725706506274192425043867981484896313502 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1500000) Primes: RFBsize:230209, AFBsize:230668, largePrimes:6776674 encountered Relations: rels:6460557, finalFF:550004 Max relations in full relation-set: 28 Initial matrix: 460957 x 550004 with sparse part having weight 33437232. Pruned matrix : 373838 x 376206 with weight 17048281. Total sieving time: 13.36 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 14.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 26, 2007

By Yousuke Koide
(10¹⁷⁹¹-1)/9 is divisible by 430713366297695220680641963_<27>
(10¹⁸²⁷-1)/9 is divisible by 223755556979749662730993077361_<30>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (6th)

By Bruce Dodson
(10³⁰¹-1)/9 is divisible by 1141240390081433457327371568501745249133720840602413587_<55>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (5th)

By Yousuke Koide
(10¹⁷⁰⁷-1)/9 is divisible by 75920820144562528214807220511_<29>
(10¹⁷¹³-1)/9 is divisible by 21378384423167366346901350575839_<32>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶⁷-13)/9 = (4)₁₆₆3_<167> = 7 · 199 · 178417 · C159
C159 = P73 · P87
P73 = 1485476151933583531111398308948380526129750464603540854114915552692816459_<73>
P87 = 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017_<87>

Number: n N=178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803 ( 159 digits) SNFS difficulty: 167 digits. Divisors found: prp73 factor: 1485476151933583531111398308948380526129750464603540854114915552692816459 prp87 factor: 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017 elapsed time 02:46:27 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 82.93 hours. Scaled time: 108.55 units (timescale=1.309). Factorization parameters were as follows: name: KA_4_166_3 n: 178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803 skew: 1.01 deg: 5 c5: 25 c0: -26 m: 2000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3900397) Primes: RFBsize:230209, AFBsize:230867, largePrimes:7730813 encountered Relations: rels:7172093, finalFF:452321 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 82.63 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,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 82.93 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 25, 2007 (3rd)

By Sinkiti Sibata / GGNFS
(4·10¹⁶¹+41)/9 = (4)₁₆₀9_<161> = 18094688609_<11> · 26999490049546734407_<20> · C131
C131 = P57 · P75
P57 = 661800895912546464100385070921509481515371228023099756833_<57>
P75 = 137462252416217059157918563636603097318468429817984026396850545706670319831_<75>

Number: 44449_161 N=90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223 ( 131 digits) SNFS difficulty: 161 digits. Divisors found: r1=661800895912546464100385070921509481515371228023099756833 (pp57) r2=137462252416217059157918563636603097318468429817984026396850545706670319831 (pp75) Version: GGNFS-0.77.1-20060722-nocona Total time: 83.42 hours. Scaled time: 166.08 units (timescale=1.991). Factorization parameters were as follows: name: 44449_161 n: 90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223 m: 100000000000000000000000000000000 c5: 40 c0: 41 skew: 1 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4950001) Primes: RFBsize:315948, AFBsize:314247, largePrimes:6029218 encountered Relations: rels:6254224, finalFF:838574 Max relations in full relation-set: 32 Initial matrix: 630261 x 838574 with sparse part having weight 63869247. Pruned matrix : 474489 x 477704 with weight 46325545. Total sieving time: 79.60 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.37 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 83.42 hours. --------- CPU info (if available) ----------

Dec 25, 2007 (2nd)

By Jo Yeong Uk / GGNFS
9·10¹⁸¹-7 = 8(9)₁₈₀3_<182> = 3613 · 3761 · 17011 · 2340581 · 730684027 · 15300750882422633_<17> · 979400478501517858241_<21> · C119
C119 = P53 · P66
P53 = 16940272774462961564775996098870506033529998386074873_<53>
P66 = 896797988999442350354441292775914106811664777578919757946243069497_<66>

Number: 89993_181 N=15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881 ( 119 digits) Divisors found: r1=16940272774462961564775996098870506033529998386074873 (pp53) r2=896797988999442350354441292775914106811664777578919757946243069497 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 38.34 hours. Scaled time: 82.16 units (timescale=2.143). Factorization parameters were as follows: name: 89993_181 n: 15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881 skew: 98114.36 # norm 2.21e+16 c5: 31560 c4: -1924665624 c3: -412313060325580 c2: 47672706443648087839 c1: 1442560992222373548243522 c0: -146358796049818815151457984880 # alpha -6.24 Y1: 3744248581117 Y0: -54512483709568246234133 # Murphy_E 3.34e-10 # M 5312090155304946753032180946674168126337529924282533139667763695347823533748345268463219266442595271493810276031748175 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4125001) Primes: RFBsize:315948, AFBsize:316143, largePrimes:7687286 encountered Relations: rels:7809081, finalFF:793940 Max relations in full relation-set: 28 Initial matrix: 632175 x 793940 with sparse part having weight 66592823. Pruned matrix : 496253 x 499477 with weight 40203065. Polynomial selection time: 2.37 hours. Total sieving time: 34.05 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.57 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 38.34 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

Dec 25, 2007

The factor table of 699...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 24, 2007

By Robert Backstrom / GGNFS, Msieve
(64·10¹⁶⁹-1)/9 = 7(1)_169<170> = 191 · 227 · 23599 · C161
C161 = P68 · P94
P68 = 11931889546918933708321958997600760626322617766055953766899623909449_<68>
P94 = 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373_<94>

Number: n N=69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477 ( 161 digits) SNFS difficulty: 171 digits. Divisors found: Mon Dec 24 19:01:19 2007 prp68 factor: 11931889546918933708321958997600760626322617766055953766899623909449 Mon Dec 24 19:01:19 2007 prp94 factor: 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373 Mon Dec 24 19:01:19 2007 elapsed time 01:27:33 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 72.40 hours. Scaled time: 131.56 units (timescale=1.817). Factorization parameters were as follows: name: KA_7_1_169 n: 69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477 skew: 0.35 deg: 5 c5: 1 c0: -5 m: 20000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4900001) Primes: RFBsize:250150, AFBsize:249616, largePrimes:7898818 encountered Relations: rels:7354029, finalFF:555685 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 72.21 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 72.40 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Dec 23, 2007 (5th)

By matsui / GGNFS
3·10¹⁶⁶+1 = 3(0)₁₆₅1_<167> = 19² · 31 · 373 · 193939 · 23755628747941_<14> · 447212374355192497_<18> · C124
C124 = P45 · P79
P45 = 625649191871122082626948379908529671729699051_<45>
P79 = 5575285937796913330137969587393113913079322142661733106598322245299860531890319_<79>

N=3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269 ( 124 digits) SNFS difficulty: 166 digits. Divisors found: r1=625649191871122082626948379908529671729699051 (pp45) r2=5575285937796913330137969587393113913079322142661733106598322245299860531890319 (pp79) Version: GGNFS-0.77.1-20060513-prescott Total time: 108.27 hours. Scaled time: 184.28 units (timescale=1.702). Factorization parameters were as follows: n: 3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269 m: 1000000000000000000000000000000000 c5: 30 c0: 1 skew: 0.51 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5200001) Primes: RFBsize:348513, AFBsize:347321, largePrimes:5907563 encountered Relations: rels:6145608, finalFF:870306 Max relations in full relation-set: 28 Initial matrix: 695901 x 870306 with sparse part having weight 52151957. Pruned matrix : 553239 x 556782 with weight 35119544. Total sieving time: 103.81 hours. Total relation processing time: 0.19 hours. Matrix solve time: 4.08 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 108.27 hours.

Dec 23, 2007 (4th)

By Sinkiti Sibata / GGNFS
(22·10¹⁶¹-1)/3 = 7(3)_161<162> = 73 · 34653533 · 22935196665910109914667553700279_<32> · C122
C122 = P53 · P69
P53 = 15456307151502000419816734779747252856782558221670037_<53>
P69 = 817754305715924564199835791161046377202886980231427415903294669859419_<69>

Number: 73333_161 N=12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503 ( 122 digits) SNFS difficulty: 162 digits. Divisors found: r1=15456307151502000419816734779747252856782558221670037 (pp53) r2=817754305715924564199835791161046377202886980231427415903294669859419 (pp69) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 94.57 hours. Scaled time: 64.40 units (timescale=0.681). Factorization parameters were as follows: name: 73333_161 n: 12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503 m: 100000000000000000000000000000000 c5: 220 c0: -1 skew: 0.34 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4550001) Primes: RFBsize:315948, AFBsize:315952, largePrimes:5839234 encountered Relations: rels:5995706, finalFF:784221 Max relations in full relation-set: 32 Initial matrix: 631967 x 784221 with sparse part having weight 49430510. Pruned matrix : 512955 x 516178 with weight 33232195. Total sieving time: 82.14 hours. Total relation processing time: 0.43 hours. Matrix solve time: 11.76 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 94.57 hours. --------- CPU info (if available) ----------

5·10¹⁶⁷+9 = 5(0)₁₆₆9_<168> = 17 · 1989241 · 4503242489106295715733929_<25> · 13375753468061863141381463203_<29> · C108
C108 = P33 · P75
P33 = 247594231851496673861477854899257_<33>
P75 = 991401494836260862208699840210242066186026283682422229091025681417922365483_<75>

Number: 50009_167 N=245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131 ( 108 digits) SNFS difficulty: 167 digits. Divisors found: r1=247594231851496673861477854899257 (pp33) r2=991401494836260862208699840210242066186026283682422229091025681417922365483 (pp75) Version: GGNFS-0.77.1-20060722-nocona Total time: 148.51 hours. Scaled time: 295.68 units (timescale=1.991). Factorization parameters were as follows: name: 50009_167 n: 245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131 m: 1000000000000000000000000000000000 c5: 500 c0: 9 skew: 0.45 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 7250001) Primes: RFBsize:380800, AFBsize:380707, largePrimes:6144009 encountered Relations: rels:6397329, finalFF:900175 Max relations in full relation-set: 32 Initial matrix: 761574 x 900175 with sparse part having weight 67509735. Pruned matrix : 652300 x 656171 with weight 49587514. Total sieving time: 142.12 hours. Total relation processing time: 0.32 hours. Matrix solve time: 5.80 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 148.51 hours. --------- CPU info (if available) ----------

Dec 23, 2007 (3rd)

By Jo Yeong Uk / GGNFS
2·10¹⁸⁷+9 = 2(0)₁₈₆9_<188> = 61 · 149 · 283 · 70663 · 2939271579080203_<16> · 4012670006992512529_<19> · 5937247290902120471857247_<25> · C118
C118 = P48 · P70
P48 = 875378053458562890900671686629987206094799966703_<48>
P70 = 1795070177818256857278501924746661172178297270528928854534971402770967_<70>

Number: 20009_187 N=1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801 ( 118 digits) Divisors found: r1=875378053458562890900671686629987206094799966703 (pp48) r2=1795070177818256857278501924746661172178297270528928854534971402770967 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 33.41 hours. Scaled time: 71.01 units (timescale=2.125). Factorization parameters were as follows: name: 20009_187 n: 1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801 skew: 86841.90 # norm 2.08e+16 c5: 18720 c4: 8005758744 c3: -417143604761414 c2: -54242084718394161427 c1: 1422581424753045528714126 c0: 43918391624543280113635161840 # alpha -6.35 Y1: 1252807503029 Y0: -38440854919115622102169 # Murphy_E 3.88e-10 # M 1529114244625491084620152441929551187310300433953474676067635486861415835076684651925957412555777624572292435341208442 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 100 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3975001) Primes: RFBsize:315948, AFBsize:316044, largePrimes:7583161 encountered Relations: rels:7616240, finalFF:734012 Max relations in full relation-set: 28 Initial matrix: 632072 x 734011 with sparse part having weight 59496583. Pruned matrix : 544994 x 548218 with weight 38635632. Total sieving time: 31.36 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.72 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 33.41 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Total of 4 processors activated (19246.11 BogoMIPS).

Dec 23, 2007 (2nd)

By Robert Backstrom / GMP-ECM
(13·10¹⁶⁵-31)/9 = 1(4)₁₆₄1_<166> = 11 · 499 · 1319876500333999_<16> · C147
C147 = P40 · P107
P40 = 1994429019434361543756357833325269071763_<40>
P107 = 99966786327320553004552683264048083299808115979086757765172472797852861187379110833799751735350193567159837_<107>

Dec 23, 2007

By Yousuke Koide
(10¹⁴⁶⁵-1)/9 is divisible by 750351062900043426795315702791_<30>
(10¹⁵⁴⁷-1)/9 is divisible by 223088287829064817231566124802627_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 22, 2007

By Robert Backstrom / GGNFS, Msieve
5·10¹⁵³+9 = 5(0)₁₅₂9_<154> = 113 · 283 · C150
C150 = P64 · P86
P64 = 9652395741655011049538026702985684108326820233080272800634433481_<64>
P86 = 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891_<86>

Number: n N=156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571 ( 150 digits) SNFS difficulty: 154 digits. Divisors found: Sat Dec 22 17:46:28 2007 prp64 factor: 9652395741655011049538026702985684108326820233080272800634433481 Sat Dec 22 17:46:28 2007 prp86 factor: 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891 Sat Dec 22 17:46:28 2007 elapsed time 00:41:58 (Msieve 1.31) Version: GGNFS-0.77.1-20051202-athlon Total time: 20.36 hours. Scaled time: 35.68 units (timescale=1.752). Factorization parameters were as follows: name: KA_5_0_152_9 n: 156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571 type: snfs skew: 1.41 deg: 5 c5: 8 c0: 45 m: 5000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1200000) Primes: RFBsize:216816, AFBsize:215956, largePrimes:6188331 encountered Relations: rels:5704176, finalFF:531554 Max relations in full relation-set: 28 Initial matrix: 432837 x 531554 with sparse part having weight 24767036. Pruned matrix : Total sieving time: 20.20 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,154,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 20.36 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 21, 2007 (3rd)

By Yousuke Koide
(10¹³³⁹-1)/9 is divisible by 5775107139441156343356533814929_<31>
(10¹³⁵¹-1)/9 is divisible by 1782854636817021657923017573_<28>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 21, 2007 (2nd)

By NFSNet
(10²³⁹-1)/9 = (1)_239<239> = 479 · 142847911 · C228
C228 = P54 · P81 · P94
P54 = 383155477843726029783939406113226468701730728790004161_<54>
P81 = 128780300340244872385688233345188210841783983757299260103530718169486826135819357_<81>
P94 = 3290967632861131703281828943635774383301940171982919699073443165222894023742681701403432993547_<94>
Reference: NFSNet current status

Dec 21, 2007

By Robert Backstrom / GGNFS, Msieve
5·10¹⁶³+9 = 5(0)₁₆₂9_<164> = 470209 · 29802628633_<11> · C148
C148 = P39 · P44 · P66
P39 = 994274499440732115855225384785607465089_<39>
P44 = 20388243227799757288129029804812187656347787_<44>
P66 = 176010423833552850724204320884474640196768850687932515195507552179_<66>

Number: n N=3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697 ( 148 digits) SNFS difficulty: 164 digits. Divisors found: Fri Dec 21 19:06:29 2007 prp39 factor: 994274499440732115855225384785607465089 Fri Dec 21 19:06:29 2007 prp44 factor: 20388243227799757288129029804812187656347787 Fri Dec 21 19:06:29 2007 prp66 factor: 176010423833552850724204320884474640196768850687932515195507552179 Fri Dec 21 19:06:29 2007 elapsed time 01:29:29 (Msieve 1.31) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 46.82 hours. Scaled time: 61.47 units (timescale=1.313). Factorization parameters were as follows: name: KA_5_0_162_9 n: 3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697 skew: 1.41 deg: 5 c5: 8 c0: 45 m: 500000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2200000) Primes: RFBsize:230209, AFBsize:229217, largePrimes:7357077 encountered Relations: rels:6869781, finalFF:531314 Max relations in full relation-set: 28 Initial matrix: 459491 x 531314 with sparse part having weight 41024110. Pruned matrix : 405664 x 408025 with weight 28167530. Total sieving time: 46.52 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,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 46.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 20, 2007 (2nd)

By Sinkiti Sibata / GGNFS
5·10¹⁵⁷+9 = 5(0)₁₅₆9_<158> = 1097 · 14897 · 26348627 · 158905115827_<12> · 230706227803_<12> · C121
C121 = P59 · P63
P59 = 25360542995799645970199393340105446955335067305527210019419_<59>
P63 = 124896659843040259553684977555818906011332891068066978344194417_<63>

Number: 50009_157 N=3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723 ( 121 digits) SNFS difficulty: 157 digits. Divisors found: r1=25360542995799645970199393340105446955335067305527210019419 (pp59) r2=124896659843040259553684977555818906011332891068066978344194417 (pp63) Version: GGNFS-0.77.1-20060513-k8 Total time: 49.75 hours. Scaled time: 99.65 units (timescale=2.003). Factorization parameters were as follows: name: 50009_157 n: 3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723 m: 10000000000000000000000000000000 c5: 500 c0: 9 skew: 0.45 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3200001) Primes: RFBsize:216816, AFBsize:216721, largePrimes:5704293 encountered Relations: rels:5645688, finalFF:500017 Max relations in full relation-set: 28 Initial matrix: 433604 x 500017 with sparse part having weight 46100082. Pruned matrix : 406183 x 408415 with weight 34369135. Total sieving time: 46.98 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.40 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 49.75 hours. --------- CPU info (if available) ----------

Dec 20, 2007

By Robert Backstrom / GGNFS, Msieve
5·10¹⁵⁹+9 = 5(0)₁₅₈9_<160> = 158855819 · C152
C152 = P51 · P101
P51 = 595062504831659452988979151082530531460782679178587_<51>
P101 = 52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753_<101>

Number: n N=31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011 ( 152 digits) SNFS difficulty: 160 digits. Divisors found: r1=595062504831659452988979151082530531460782679178587 (pp51) r2=52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 20.39 hours. Scaled time: 37.07 units (timescale=1.818). Factorization parameters were as follows: name: KA_5_0_158_9 n: 31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011 skew: 1.78 deg: 5 c5: 1 c0: 18 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:6939749 encountered Relations: rels:6405566, finalFF:494197 Max relations in full relation-set: 48 Initial matrix: 433819 x 494197 with sparse part having weight 37620448. Pruned matrix : 385615 x 387848 with weight 23915069. Total sieving time: 19.02 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.08 hours. Total square root time: 0.14 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 20.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

8·10¹⁶³-7 = 7(9)₁₆₂3_<164> = 1511 · 9661 · 321227 · 564463 · C146
C146 = P42 · P104
P42 = 725182024346650930487852356735252779350207_<42>
P104 = 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569_<104>

Number: n N=30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783 ( 146 digits) SNFS difficulty: 165 digits. Divisors found: Thu Dec 20 18:40:55 2007 prp42 factor: 725182024346650930487852356735252779350207 Thu Dec 20 18:40:55 2007 prp104 factor: 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569 Thu Dec 20 18:40:55 2007 elapsed time 02:14:03 (Msieve 1.31) Version: GGNFS-0.77.1-20051202-athlon Total time: 113.19 hours. Scaled time: 198.19 units (timescale=1.751). Factorization parameters were as follows: name: KA_7_9_162_3 n: 30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783 type: snfs skew: 0.49 deg: 5 c5: 2 c0: -175 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4400001) Primes: RFBsize:230209, AFBsize:231247, largePrimes:7814161 encountered Relations: rels:7249012, finalFF:516556 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 112.81 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 113.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 19, 2007 (5th)

By Yousuke Koide
(10¹²⁴⁹-1)/9 is divisible by 3859327619352771895471324837_<28>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 19, 2007 (4th)

By Jo Yeong Uk / GMP-ECM
5·10¹⁶²+9 = 5(0)₁₆₁9_<163> = 7 · 29² · 271229879065601402201623_<24> · C136
C136 = P35 · P101
P35 = 64374435181365818315554180691915647_<35>
P101 = 48643521375868913517679138570941692047144478517809618044912143356711058007954967110653981808106775647_<101>

Dec 19, 2007 (3rd)

By matsui / GGNFS
(7·10¹⁶⁶+11)/9 = (7)₁₆₅9_<166> = 3 · 40361 · 205111360920457_<15> · 12389475956090072848518619_<26> · C122
C122 = P47 · P75
P47 = 55943227542338151602426973986475076889992624589_<47>
P75 = 451837410354294038053223198387566184140151017305302109616973764868158183999_<75>

N=25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411 ( 122 digits) SNFS difficulty: 166 digits. Divisors found: r1=55943227542338151602426973986475076889992624589 (pp47) r2=451837410354294038053223198387566184140151017305302109616973764868158183999 (pp75) Version: GGNFS-0.77.1-20060513-prescott Total time: 10.74 hours. Scaled time: 18.27 units (timescale=1.701). Factorization parameters were as follows: n: 25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411 m: 1000000000000000000000000000000000 c5: 70 c0: 11 skew: 0.69 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 6000001) Primes: , , largePrimes:5871705 encountered Relations: rels:5969485, finalFF:743203 Max relations in full relation-set: 28 Initial matrix: 696897 x 743203 with sparse part having weight 52810271. Pruned matrix : 665688 x 669236 with weight 44065470. Total sieving time: 2.91 hours. Total relation processing time: 0.01 hours. Matrix solve time: 7.59 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 10.74 hours.

Dec 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS
5·10¹⁵⁶+9 = 5(0)₁₅₅9_<157> = 7 · 37447 · 28194483512088014904108943_<26> · C126
C126 = P62 · P64
P62 = 74881270812473695723895111402915691073452855235176557355117707_<62>
P64 = 9034780048660293802053456177468412100175147936351538480358818021_<64>

Number: 50009_156 N=676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847 ( 126 digits) SNFS difficulty: 156 digits. Divisors found: r1=74881270812473695723895111402915691073452855235176557355117707 (pp62) r2=9034780048660293802053456177468412100175147936351538480358818021 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 32.37 hours. Scaled time: 64.84 units (timescale=2.003). Factorization parameters were as follows: name: 50009_156 n: 676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847 m: 10000000000000000000000000000000 c5: 50 c0: 9 skew: 0.71 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2600001) Primes: RFBsize:216816, AFBsize:215821, largePrimes:5559380 encountered Relations: rels:5479029, finalFF:518470 Max relations in full relation-set: 28 Initial matrix: 432702 x 518470 with sparse part having weight 40228570. Pruned matrix : 380168 x 382395 with weight 26863487. Total sieving time: 30.33 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.72 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.37 hours. --------- CPU info (if available) ----------

Dec 19, 2007

By Robert Backstrom / GGNFS, Msieve
5·10¹⁴⁷+9 = 5(0)₁₄₆9_<148> = C148
C148 = P40 · P108
P40 = 5849697884884838262743075248501338289883_<40>
P108 = 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923_<108>

Number: n N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 148 digits) SNFS difficulty: 149 digits. Divisors found: Wed Dec 19 02:59:00 2007 prp40 factor: 5849697884884838262743075248501338289883 Wed Dec 19 02:59:00 2007 prp108 factor: 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923 Wed Dec 19 02:59:00 2007 elapsed time 00:54:34 (Msieve 1.31) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 12.29 hours. Scaled time: 16.07 units (timescale=1.308). Factorization parameters were as follows: name: KA_5_0_146_9 n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 skew: 2.24 deg: 5 c5: 4 c0: 225 m: 500000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1500001) Primes: RFBsize:203362, AFBsize:203297, largePrimes:6971350 encountered Relations: rels:6423924, finalFF:479679 Max relations in full relation-set: 28 Initial matrix: 406723 x 479679 with sparse part having weight 30923173. Pruned matrix : Total sieving time: 12.09 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 12.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 18, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM
5·10¹⁶⁴+9 = 5(0)₁₆₃9_<165> = C165
C165 = P79 · P86
P79 = 6673964901781837641922867159706054031558290898862034367879686441388466755506249_<79>
P86 = 74917984640061309718805919117074967560324362619058281263115508699855177428830489506241_<86>

Number: 50009_164 N=500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 165 digits) SNFS difficulty: 165 digits. Divisors found: r1=6673964901781837641922867159706054031558290898862034367879686441388466755506249 (pp79) r2=74917984640061309718805919117074967560324362619058281263115508699855177428830489506241 (pp86) Version: GGNFS-0.77.1-20050930-nocona Total time: 39.42 hours. Scaled time: 84.59 units (timescale=2.146). Factorization parameters were as follows: n: 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 m: 1000000000000000000000000000000000 c5: 1 c0: 18 skew: 1.78 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2500000, 4600001) Primes: RFBsize:348513, AFBsize:348406, largePrimes:6566352 encountered Relations: rels:6735729, finalFF:809660 Max relations in full relation-set: 28 Initial matrix: 696986 x 809660 with sparse part having weight 54958042. Pruned matrix : 606950 x 610498 with weight 38013089. Total sieving time: 37.13 hours. Total relation processing time: 0.10 hours. Matrix solve time: 2.13 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000 total time: 39.42 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁸⁵+9 = 5(0)₁₈₄9_<186> = C186
C186 = P42 · C144
P42 = 862676558302067280404855791214660371447819_<42>
C144 = [579591499488646557153454224836516440632324855138225561082733176963781513205559091433257936622764264592554118739834167338788722441133338317646011_<144>]

Dec 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS
5·10¹⁵⁴+9 = 5(0)₁₅₃9_<155>= 829 · 15683 · 56596823 · 44630287349_<11> · C130
C130 = P58 · P72
P58 = 6547416756766895807011708792092633881889587619560266369321_<58>
P72 = 232538362293215384924110022839616818354212477256510811617282792627275661_<72>

Number: 50009_154 N=1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181 ( 130 digits) SNFS difficulty: 155 digits. Divisors found: r1=6547416756766895807011708792092633881889587619560266369321 (pp58) r2=232538362293215384924110022839616818354212477256510811617282792627275661 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 32.09 hours. Scaled time: 64.08 units (timescale=1.997). Factorization parameters were as follows: name: 50009_154 n: 1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181 m: 10000000000000000000000000000000 c5: 1 c0: 18 skew: 1.78 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2600001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:5911757 encountered Relations: rels:6144438, finalFF:787955 Max relations in full relation-set: 28 Initial matrix: 433819 x 787955 with sparse part having weight 63391684. Pruned matrix : 273376 x 275609 with weight 35731953. Total sieving time: 30.69 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.09 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.09 hours. --------- CPU info (if available) ----------

Dec 18, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve
5·10¹⁶³+3 = 5(0)₁₆₂3_<164> = 29 · 227 · 1372379 · 3452401427_<10> · C145
C145 = P58 · P87
P58 = 1652368488234263596749387089016071429414818510198454291329_<58>
P87 = 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013_<87>

Number: n N=1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277 ( 145 digits) SNFS difficulty: 164 digits. Divisors found: Tue Dec 18 13:14:30 2007 prp58 factor: 1652368488234263596749387089016071429414818510198454291329 Tue Dec 18 13:14:30 2007 prp87 factor: 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013 Tue Dec 18 13:14:30 2007 elapsed time 01:41:34 (Msieve 1.31) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 65.55 hours. Scaled time: 85.80 units (timescale=1.309). Factorization parameters were as follows: name: KA_5_0_162_3 n: 1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277 skew: 1.13 deg: 5 c5: 8 c0: 15 m: 500000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100001) Primes: RFBsize:230209, AFBsize:229672, largePrimes:7196433 encountered Relations: rels:6672971, finalFF:503221 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 65.18 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 65.55 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

5·10¹⁴⁵+9 = 5(0)₁₄₄9_<146> = 480587 · 664114531 · 173304257326374916002763_<24> · C108
C108 = P40 · P69
P40 = 8011859098238196250376857716817447795633_<40>
P69 = 112826851275727796887800559483225541997057785219800577879840211604843_<69>

Number: n N=903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619 ( 108 digits) SNFS difficulty: 145 digits. Divisors found: Tue Dec 18 15:02:49 2007 prp40 factor: 8011859098238196250376857716817447795633 Tue Dec 18 15:02:49 2007 prp69 factor: 112826851275727796887800559483225541997057785219800577879840211604843 Tue Dec 18 15:02:49 2007 elapsed time 00:24:54 (Msieve 1.31) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.79 hours. Scaled time: 8.75 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_0_144_9 n: 903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619 skew: 1.12 deg: 5 c5: 5 c0: 9 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 900000) Primes: RFBsize:183072, AFBsize:182621, largePrimes:6411156 encountered Relations: rels:5849768, finalFF:448390 Max relations in full relation-set: 28 Initial matrix: 365759 x 448390 with sparse part having weight 26854576. Pruned matrix : 294774 x 296666 with weight 13333677. Total sieving time: 4.67 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 4.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Dec 18, 2007

By Yousuke Koide
(10¹¹⁷¹-1)/9 is divisible by 822720687271610738727673132529_<30>, cofactor is prime
(10¹¹⁹³-1)/9 is divisible by 14202873041760299228830573_<26>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (3rd)

By Yousuke Koide
(10¹⁵⁰⁹-1)/9 is divisible by 276617318087890951973712854116609_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS
5·10¹¹⁶+9 = 5(0)₁₁₅9_<117> = 5647 · 14738747 · C106
C106 = P37 · P70
P37 = 1770527491110016131038045568525078001_<37>
P70 = 3393039989462346591698405537211579666741526697212892785900831616289301_<70>

Number: 50009_116 N=6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301 ( 106 digits) SNFS difficulty: 116 digits. Divisors found: r1=1770527491110016131038045568525078001 (pp37) r2=3393039989462346591698405537211579666741526697212892785900831616289301 (pp70) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.65 hours. Scaled time: 1.11 units (timescale=0.674). Factorization parameters were as follows: name: 50009_116 n: 6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301 m: 100000000000000000000000 c5: 50 c0: 9 skew: 0.71 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:64058, largePrimes:1928320 encountered Relations: rels:1872426, finalFF:132412 Max relations in full relation-set: 28 Initial matrix: 113221 x 132412 with sparse part having weight 9758667. Pruned matrix : 104806 x 105436 with weight 6199905. Total sieving time: 1.39 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.17 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.65 hours. --------- CPU info (if available) ----------

5·10¹³⁷+9 = 5(0)₁₃₆9_<138> = 97 · 1506773568889_<13> · 226074463554510734010057673_<27> · C98
C98 = P38 · P60
P38 = 54141127725421474038977984368371957931_<38>
P60 = 279493344149482372551112704180571406141518303948937390507771_<60>

Number: 50009_137 N=15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801 ( 98 digits) SNFS difficulty: 137 digits. Divisors found: r1=54141127725421474038977984368371957931 (pp38) r2=279493344149482372551112704180571406141518303948937390507771 (pp60) Version: GGNFS-0.77.1-20060513-k8 Total time: 12.19 hours. Scaled time: 24.20 units (timescale=1.985). Factorization parameters were as follows: name: 50009_137 n: 15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801 m: 1000000000000000000000000000 c5: 500 c0: 9 skew: 0.45 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1975001) Primes: RFBsize:78498, AFBsize:64083, largePrimes:1684652 encountered Relations: rels:1727895, finalFF:191071 Max relations in full relation-set: 28 Initial matrix: 142648 x 191071 with sparse part having weight 20882416. Pruned matrix : 131206 x 131983 with weight 12913225. Total sieving time: 11.87 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.16 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 12.19 hours. --------- CPU info (if available) ----------

5·10¹⁵¹+9 = 5(0)₁₅₀9_<152> = 17 · 43 · 107 · C147
C147 = P48 · P100
P48 = 334673882571236023305008947620488003064113918729_<48>
P100 = 1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513_<100>

Number: 50009_151 N=639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977 ( 147 digits) SNFS difficulty: 151 digits. Divisors found: r1=334673882571236023305008947620488003064113918729 (pp48) r2=1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513 (pp100) Version: GGNFS-0.77.1-20060513-k8 Total time: 20.92 hours. Scaled time: 41.16 units (timescale=1.967). Factorization parameters were as follows: name 50009_151 n: 639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977 m: 1000000000000000000000000000000 c5: 50 c0: 9 skew: 0.71 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 1900001) Primes: RFBsize:176302, AFBsize:175768, largePrimes:5442675 encountered Relations: rels:5368300, finalFF:498395 Max relations in full relation-set: 28 Initial matrix: 352135 x 498395 with sparse part having weight 42380181. Pruned matrix : 282161 x 283985 with weight 22301234. Total sieving time: 19.66 hours. Total relation processing time: 0.13 hours. Matrix solve time: 1.00 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 20.92 hours. --------- CPU info (if available) ----------

Dec 17, 2007

By Jo Yeong Uk / GGNFS
5·10¹³⁸+9 = 5(0)₁₃₇9_<139> = 7 · 67 · 24062444319260058179401_<23> · C114
C114 = P45 · P69
P45 = 946212734975879332729540202137182929419049849_<45>
P69 = 468240129107916666081642626977725725851067323112806555638980157404389_<69>

Number: 50009_138 N=443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261 ( 114 digits) SNFS difficulty: 140 digits. Divisors found: r1=946212734975879332729540202137182929419049849 (pp45) r2=468240129107916666081642626977725725851067323112806555638980157404389 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.63 hours. Scaled time: 9.87 units (timescale=2.129). Factorization parameters were as follows: n: 443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261 m: 10000000000000000000000000000 c5: 1 c0: 180 skew: 2.83 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1000001) Primes: RFBsize:107126, AFBsize:107118, largePrimes:2193538 encountered Relations: rels:2294860, finalFF:267501 Max relations in full relation-set: 28 Initial matrix: 214308 x 267501 with sparse part having weight 20336589. Pruned matrix : 188484 x 189619 with weight 11495582. Total sieving time: 4.48 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 4.63 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁴⁹+9 = 5(0)₁₄₈9_<150> = 614655261608425773017_<21> · C129
C129 = P43 · P87
P43 = 1292831320258423031896200514838978324604313_<43>
P87 = 629211332393361618328576188689966621539549657057208953485058442782747222654866355168729_<87>

Number: 50009_149 N=813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177 ( 129 digits) SNFS difficulty: 150 digits. Divisors found: r1=1292831320258423031896200514838978324604313 (pp43) r2=629211332393361618328576188689966621539549657057208953485058442782747222654866355168729 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.28 hours. Scaled time: 24.19 units (timescale=2.145). Factorization parameters were as follows: n: 813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177 m: 1000000000000000000000000000000 c5: 1 c0: 18 skew: 1.78 type: snfs 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, 1650001) Primes: RFBsize:135072, AFBsize:134903, largePrimes:3896038 encountered Relations: rels:4055635, finalFF:434303 Max relations in full relation-set: 28 Initial matrix: 270042 x 434303 with sparse part having weight 42347910. Pruned matrix : 218215 x 219629 with weight 20005906. Total sieving time: 10.98 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.22 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 11.28 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007 (4th)

By Sinkiti Sibata / GGNFS
5·10¹²¹+9 = 5(0)₁₂₀9_<122> = 401 · C120
C120 = P39 · P81
P39 = 234394740470022334833839226247804877881_<39>
P81 = 531958520279564508033197824266783726238632647326464705045488524626649705389905089_<81>

Number: 50009_121 N=124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409 ( 120 digits) SNFS difficulty: 121 digits. Divisors found: r1=234394740470022334833839226247804877881 (pp39) r2=531958520279564508033197824266783726238632647326464705045488524626649705389905089 (pp81) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.07 hours. Scaled time: 4.13 units (timescale=1.992). Factorization parameters were as follows: name: 50009_121 n: 124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409 m: 1000000000000000000000000 c5: 50 c0: 9 skew: 0.71 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64058, largePrimes:2256398 encountered Relations: rels:2489942, finalFF:350248 Max relations in full relation-set: 28 Initial matrix: 113221 x 350248 with sparse part having weight 32201932. Pruned matrix : 75006 x 75636 with weight 5986172. Total sieving time: 1.95 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.07 hours. --------- CPU info (if available) ----------

5·10¹⁰⁷+9 = 5(0)₁₀₆9_<108> = 19 · C107
C107 = P35 · P73
P35 = 22161612064368328651072431710802457_<35>
P73 = 1187449243189082427047892522175799526276103441537325771419337450292326123_<73>

Number: 50009_107 N=26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211 ( 107 digits) SNFS difficulty: 107 digits. Divisors found: r1=22161612064368328651072431710802457 (pp35) r2=1187449243189082427047892522175799526276103441537325771419337450292326123 (pp73) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.95 hours. Scaled time: 1.31 units (timescale=0.674). Factorization parameters were as follows: name: 50009_107 n: 26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211 m: 1000000000000000000000 c5: 500 c0: 9 skew: 0.45 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:64083, largePrimes:2414537 encountered Relations: rels:2970085, finalFF:672208 Max relations in full relation-set: 28 Initial matrix: 113248 x 672208 with sparse part having weight 51031416. Pruned matrix : 58155 x 58785 with weight 4968824. Total sieving time: 1.78 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.95 hours. --------- CPU info (if available) ----------

5·10¹¹⁴+9 = 5(0)₁₁₃9_<115> = 7 · 83 · 463 · 48623 · C105
C105 = P38 · P67
P38 = 70541614319082877066125526339209355501_<38>
P67 = 5419082164403195929289385747756719945734828037540124137574223619561_<67>

Number: 50009_114 N=382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061 ( 105 digits) SNFS difficulty: 115 digits. Divisors found: r1=70541614319082877066125526339209355501 (pp38) r2=5419082164403195929289385747756719945734828037540124137574223619561 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.67 hours. Scaled time: 1.13 units (timescale=0.674). Factorization parameters were as follows: name: 50009_114 n: 382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061 m: 100000000000000000000000 c5: 1 c0: 18 skew: 1.78 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:63888, largePrimes:2196933 encountered Relations: rels:2439165, finalFF:379789 Max relations in full relation-set: 28 Initial matrix: 113053 x 379789 with sparse part having weight 30408564. Pruned matrix : 65611 x 66240 with weight 4277422. Total sieving time: 1.50 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.67 hours. --------- CPU info (if available) ----------

Dec 16, 2007 (3rd)

By Robert Backstrom / GMP-ECM
5·10¹⁰²+9 = 5(0)₁₀₁9_<103> = 7 · 23 · 7001 · C97
C97 = P41 · P57
P41 = 31854706908327006451053849450780933259103_<41>
P57 = 139254884403520782870512217316445103008038584589836414223_<57>

Dec 16, 2007 (2nd)

By Jo Yeong Uk / GGNFS
5·10¹³³+9 = 5(0)₁₃₂9_<134> = C134
C134 = P55 · P80
P55 = 1808856091842673778141469519200801928271629226769243833_<55>
P80 = 27641778815618891492508230793764960546620767858028425576294203682615206075499473_<80>

Number: 50009_133 N=50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 134 digits) SNFS difficulty: 135 digits. Divisors found: r1=1808856091842673778141469519200801928271629226769243833 (pp55) r2=27641778815618891492508230793764960546620767858028425576294203682615206075499473 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.70 hours. Scaled time: 5.79 units (timescale=2.145). Factorization parameters were as follows: n: 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 m: 1000000000000000000000000000 c5: 1 c0: 180 skew: 2.83 type: snfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [600000, 1150001) Primes: RFBsize:92938, AFBsize:92784, largePrimes:1635992 encountered Relations: rels:1676140, finalFF:218361 Max relations in full relation-set: 28 Initial matrix: 185786 x 218361 with sparse part having weight 11337457. Pruned matrix : 170705 x 171697 with weight 7105532. Total sieving time: 2.59 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000 total time: 2.70 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁶+9 = 5(0)₁₂₅9_<127> = 7 · 541 · C124
C124 = P62 · P62
P62 = 18583998288422002372740046473239078846323774567438627504014367_<62>
P62 = 71045331073170059497410700220270620432737612295639886159776421_<62>

Number: 50009_126 N=1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507 ( 124 digits) SNFS difficulty: 126 digits. Divisors found: r1=18583998288422002372740046473239078846323774567438627504014367 (pp62) r2=71045331073170059497410700220270620432737612295639886159776421 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.52 hours. Scaled time: 3.25 units (timescale=2.136). Factorization parameters were as follows: n: 1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507 m: 10000000000000000000000000 c5: 50 c0: 9 skew: 0.71 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [400000, 720001) Primes: RFBsize:63951, AFBsize:64058, largePrimes:1387334 encountered Relations: rels:1376239, finalFF:164736 Max relations in full relation-set: 28 Initial matrix: 128074 x 164736 with sparse part having weight 7959278. Pruned matrix : 112535 x 113239 with weight 4175510. Total sieving time: 1.46 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000 total time: 1.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁹+9 = 5(0)₁₂₈9_<130> = 1283 · 6673 · 421483 · C118
C118 = P35 · P36 · P48
P35 = 55851141761388119444538473036013289_<35>
P36 = 188165401070611685235607528162110379_<36>
P48 = 131847024827184141097638546699400890537611235187_<48>

Number: 50009_129 N=1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297 ( 118 digits) SNFS difficulty: 130 digits. Divisors found: r1=55851141761388119444538473036013289 (pp35) r2=188165401070611685235607528162110379 (pp36) r3=131847024827184141097638546699400890537611235187 (pp48) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.96 hours. Scaled time: 4.16 units (timescale=2.127). Factorization parameters were as follows: n: 1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297 m: 100000000000000000000000000 c5: 1 c0: 18 skew: 1.78 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78486, largePrimes:1556493 encountered Relations: rels:1609896, finalFF:225323 Max relations in full relation-set: 28 Initial matrix: 157051 x 225323 with sparse part having weight 11609462. Pruned matrix : 126069 x 126918 with weight 5246803. Total sieving time: 1.89 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.96 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007

By Sinkiti Sibata / PRIMO
(2·10²⁴⁰³+1)/3 is prime.

Dec 15, 2007 (4th)

By matsui / GGNFS
(5·10¹⁶⁶+7)/3 = 1(6)₁₆₅9_<167> = 38609 · 75787 · 156630091583671031730558418871436461_<36> · C122
C122 = P52 · P71
P52 = 2264388869748319451290164995673979200391552839732379_<52>
P71 = 16059767993409165566619664888931389674520944070045699328877175122292297_<71>

N=36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563 ( 122 digits) SNFS difficulty: 166 digits. Divisors found: r1=2264388869748319451290164995673979200391552839732379 (pp52) r2=16059767993409165566619664888931389674520944070045699328877175122292297 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 125.39 hours. Scaled time: 238.73 units (timescale=1.904). Factorization parameters were as follows: n: 36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563 m: 1000000000000000000000000000000000 c5: 50 c0: 7 skew: 0.67 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 6400001) Primes: RFBsize:348513, AFBsize:349596, largePrimes:6068375 encountered Relations: rels:6296703, finalFF:852370 Max relations in full relation-set: 28 Initial matrix: 698174 x 852370 with sparse part having weight 63956552. Pruned matrix : 581570 x 585124 with weight 46821531. Total sieving time: 110.75 hours. Total relation processing time: 0.15 hours. Matrix solve time: 14.13 hours. Time per square root: 0.35 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 125.39 hours.

Dec 15, 2007 (3rd)

By Yousuke Koide
(10¹³⁷⁵-1)/9 is divisible by 584213416911071661540509773751_<30>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 15, 2007 (2nd)

The factor table of 500...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 15, 2007

By Alfred Reich
10¹⁸¹³+1 is divisible by 1341949101412826358472947603971939_<34>
10¹⁹⁶⁶+1 is divisible by 4955902500081447124888466401899581_<34>
Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Dec 14, 2007 (4th)

By Yousuke Koide
(10¹³¹⁵-1)/9 is divisible by 155872807295141767753013971998423271_<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 14, 2007 (3rd)

By Sinkiti Sibata / PRIMO
(2·10²³⁶²+43)/9 is prime.

Dec 14, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(5·10¹⁶³+31)/9 = (5)₁₆₂9_<163> = 3² · 11503 · 2014594707737_<13> · C146
C146 = P35 · P44 · P68
P35 = 30188843843595259209660847329747917_<35>
P44 = 35971250079769021640351453407071430175983319_<44>
P68 = 24529244107054551003240215672832228187869914838761899129142536396667_<68>

Number: n N=882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773 ( 111 digits) Divisors found: Fri Dec 14 06:00:23 2007 prp44 factor: 35971250079769021640351453407071430175983319 Fri Dec 14 06:00:23 2007 prp68 factor: 24529244107054551003240215672832228187869914838761899129142536396667 Fri Dec 14 06:00:23 2007 elapsed time 01:21:20 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 23.38 hours. Scaled time: 40.42 units (timescale=1.729). Factorization parameters were as follows: name: KA_5_162_9 n: 882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773 skew: 19044.42 # norm 6.38e+15 c5: 111600 c4: 14885090508 c3: 145705138135436 c2: -5337155657782209549 c1: 9745908703860354342290 c0: 107907444208141710319877800 # alpha -6.45 Y1: 212966576537 Y0: -1512145107533754160601 # Murphy_E 8.60e-10 # M 496213671955529285371696094504443999209726698467323627075527118570036745236814734332119703037015817317104508841 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1200001) Primes: RFBsize:230209, AFBsize:230305, largePrimes:6818981 encountered Relations: rels:6507373, finalFF:543771 Max relations in full relation-set: 28 Initial matrix: 460599 x 543771 with sparse part having weight 35789432. Pruned matrix : Total sieving time: 23.12 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: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 23.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(4·10¹⁶¹+23)/9 = (4)₁₆₀7_<161> = 13³ · 132253376785665958621_<21> · C138
C138 = P39 · P99
P39 = 208122669820059734018270507907490349851_<39>
P99 = 734955876882058340201805409936009321630527412736093444708338848258488834565508219522142315629339181_<99>
5·10¹⁵²-9 = 4(9)₁₅₁1_<153> = 19 · 199 · 1451 · 94201 · C141
C141 = P52 · P90
P52 = 2456042554669170698593684758425118153245909492210089_<52>
P90 = 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649_<90>

Number: n N=967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761 ( 141 digits) SNFS difficulty: 152 digits. Divisors found: Fri Dec 14 22:19:20 2007 prp52 factor: 2456042554669170698593684758425118153245909492210089 Fri Dec 14 22:19:20 2007 prp90 factor: 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649 Fri Dec 14 22:19:20 2007 elapsed time 01:04:26 (Msieve 1.30) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 22.64 hours. Scaled time: 29.75 units (timescale=1.314). Factorization parameters were as follows: name: KA_4_9_151_1 n: 967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761 skew: 0.45 deg: 5 c5: 500 c0: -9 m: 1000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1100000) Primes: RFBsize:203362, AFBsize:203297, largePrimes:6755039 encountered Relations: rels:6230916, finalFF:474146 Max relations in full relation-set: 28 Initial matrix: 406726 x 474146 with sparse part having weight 31631044. Pruned matrix : 349533 x 351630 with weight 19468857. Total sieving time: 22.45 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 22.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 14, 2007

By Jo Yeong Uk / GGNFS
5·10¹⁵⁸-9 = 4(9)₁₅₇1_<159> = 192370543578919_<15> · 255761895497279_<15> · 6553146809446631_<16> · C115
C115 = P36 · P79
P36 = 916954738515527411860196269384889891_<36>
P79 = 1691210995646724198680462578472437912581425581533448011756847939729769453981971_<79>

Number: 49991_158 N=1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161 ( 115 digits) SNFS difficulty: 160 digits. Divisors found: r1=916954738515527411860196269384889891 (pp36) r2=1691210995646724198680462578472437912581425581533448011756847939729769453981971 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.62 hours. Scaled time: 54.41 units (timescale=2.124). Factorization parameters were as follows: n: 1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161 m: 100000000000000000000000000000000 c5: 1 c0: -180 skew: 2.83 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:282037, largePrimes:5639108 encountered Relations: rels:5690607, finalFF:673567 Max relations in full relation-set: 28 Initial matrix: 565247 x 673567 with sparse part having weight 41646735. Pruned matrix : 476541 x 479431 with weight 26834784. Total sieving time: 24.40 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 25.62 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126) Total of 4 processors activated (19246.09 BogoMIPS).

(67·10¹⁶¹+23)/9 = 7(4)₁₆₀7_<162> = 3 · 11 · 1399 · 1523 · 87433 · 21320365267_<11> · 40377356857463_<14> · C126
C126 = P37 · P89
P37 = 6578288242353527353007952811929293213_<37>
P89 = 21383556043195314533903891888116589234987504067784812619439791414098469151797015018035563_<89>

Dec 13, 2007

By Sinkiti Sibata / PRIMO
(2·10²¹⁷⁵-17)/3 is prime.

Dec 12, 2007

By Sinkiti Sibata / PFGW
2·10¹²⁹⁸⁴-7 and 2·10¹³⁶¹⁴-7 are PRP.

Dec 11, 2007 (2nd)

By Yousuke Koide
10¹¹²¹+1 is divisible by 69849282640264627005884025897913761023_<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 11, 2007

By Robert Backstrom / GGNFS, Msieve
5·10¹⁵⁵-9 = 4(9)₁₅₄1_<156> = 52249831 · C148
C148 = P68 · P81
P68 = 12577330540482969770037590027834896246509937898150565038352486568081_<68>
P81 = 760845786107138460535930299805308106874138122028043088814610693093595148504742881_<81>

Number: n N=9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361 ( 148 digits) SNFS difficulty: 155 digits. Divisors found: Tue Dec 11 14:10:53 2007 prp68 factor: 12577330540482969770037590027834896246509937898150565038352486568081 Tue Dec 11 14:10:53 2007 prp81 factor: 760845786107138460535930299805308106874138122028043088814610693093595148504742881 Tue Dec 11 14:10:53 2007 elapsed time 01:06:58 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.92 hours. Scaled time: 44.94 units (timescale=1.734). Factorization parameters were as follows: name: KA_4_9_154_1 n: 9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361 type: snfs skew: 1.12 deg: 5 c5: 5 c0: -9 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1200000) Primes: RFBsize:216816, AFBsize:216491, largePrimes:6390484 encountered Relations: rels:5934433, finalFF:556300 Max relations in full relation-set: 28 Initial matrix: 433373 x 556300 with sparse part having weight 28717637. Pruned matrix : 323054 x 325284 with weight 14040928. Total sieving time: 25.73 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 25.92 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 10, 2007 (5th)

By Sinkiti Sibata / PFGW
(8·10¹⁰⁷¹⁷-11)/3, (8·10¹⁴⁶⁷³-11)/3, (8·10¹⁶⁷⁵⁴-11)/3 and (8·10¹⁷⁶⁰⁶-11)/3 are PRP.

Dec 10, 2007 (4th)

By suberi / GMP-ECM
(16·10¹⁷⁶-61)/9 = 1(7)₁₇₅1_<177> = 3 · 5261 · C173
C173 = P36 · C137
P36 = 817155339792930387676948727914630841_<36>
C137 = [13784254841763201401763506838527012403768451779816402753683122065119425484587917320413953839479488490114718629521019279324075409499402757_<137>]

Dec 10, 2007 (3rd)

By Jo Yeong Uk / GGNFS
5·10¹⁶⁶-9 = 4(9)₁₆₅1_<167> = 41 · 89 · 809 · 16811 · 1289694079831_<13> · 47803986587156910009154269051461_<32> · C113
C113 = P48 · P65
P48 = 423642819486377500810088159556192139680472557229_<48>
P65 = 38574774798609590656685912133706632252046886635615382500322326219_<65>

Number: 49991_166 N=16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151 ( 113 digits) Divisors found: r1=423642819486377500810088159556192139680472557229 (pp48) r2=38574774798609590656685912133706632252046886635615382500322326219 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.00 hours. Scaled time: 42.48 units (timescale=2.124). Factorization parameters were as follows: name: 49991_166 n: 16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151 skew: 27295.93 # norm 2.18e+15 c5: 33120 c4: 4441313622 c3: -62567391423243 c2: -2850563779112809232 c1: 20403393653491258023492 c0: 412100355487556686774922021 # alpha -5.81 Y1: 642727557923 Y0: -3456530699039931079782 # Murphy_E 7.71e-10 # M 1551685654449727006542580819033466558148370987093910726938703232431161248973769563550852895364742766086059152787 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1400000, 2380001) Primes: RFBsize:203362, AFBsize:203153, largePrimes:7633589 encountered Relations: rels:7513780, finalFF:534371 Max relations in full relation-set: 28 Initial matrix: 406594 x 534371 with sparse part having weight 51341064. Pruned matrix : 315342 x 317438 with weight 31467716. Polynomial selection time: 1.06 hours. Total sieving time: 18.10 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.58 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 20.00 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Dec 10, 2007 (2nd)

By Sinkiti Sibata / GGNFS
4·10¹⁷⁹+9 = 4(0)₁₇₈9_<180> = C180
C180 = P45 · P135
P45 = 921163045658547580756150590548571589420901651_<45>
P135 = 434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659_<135>

Number: 40009_179 N=400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 180 digits) SNFS difficulty: 180 digits. Divisors found: r1=921163045658547580756150590548571589420901651 (pp45) r2=434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659 (pp135) Version: GGNFS-0.77.1-20060513-k8 Total time: 514.08 hours. Scaled time: 1025.58 units (timescale=1.995). Factorization parameters were as follows: name: 40009_179 n: 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 m: 1000000000000000000000000000000000000 c5: 2 c0: 45 skew: 1.86 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 9400001) Primes: RFBsize:501962, AFBsize:502481, largePrimes:6588779 encountered Relations: rels:7085432, finalFF:1174582 Max relations in full relation-set: 28 Initial matrix: 1004508 x 1174582 with sparse part having weight 72170055. Pruned matrix : 861753 x 866839 with weight 54190298. Total sieving time: 503.52 hours. Total relation processing time: 0.48 hours. Matrix solve time: 9.74 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 514.08 hours. --------- CPU info (if available) ----------

Dec 10, 2007

By Robert Backstrom / GGNFS, Msieve
5·10¹⁴⁶-9 = 4(9)₁₄₅1_<147> = 41 · 59 · 5970268730389741_<16> · C128
C128 = P59 · P69
P59 = 89514634314987140562070529941642327551603414368208045052321_<59>
P69 = 386764152467374483050690533716910166621405836972248541038074724385249_<69>

Number: n N=34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929 ( 128 digits) SNFS difficulty: 146 digits. Divisors found: r1=89514634314987140562070529941642327551603414368208045052321 (pp59) r2=386764152467374483050690533716910166621405836972248541038074724385249 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.86 hours. Scaled time: 12.82 units (timescale=1.447). Factorization parameters were as follows: name: KA_4_9_145_1 n: 34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929 skew: 0.71 deg: 5 c5: 50 c0: -9 m: 100000000000000000000000000000 type: snfs rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 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: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:135072, AFBsize:134503, largePrimes:6508918 encountered Relations: rels:5845525, finalFF:310973 Max relations in full relation-set: 28 Initial matrix: 269640 x 310973 with sparse part having weight 24290713. Pruned matrix : 244308 x 245720 with weight 16377793. Total sieving time: 7.07 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.51 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000 total time: 8.86 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

4·10¹⁵⁴+9 = 4(0)₁₅₃9_<155> = 17 · 13913 · 1396989572897_<13> · 61059519554988608394921409_<26> · C112
C112 = P56 · P56
P56 = 42618868918024524866536599051397923694814520254443166653_<56>
P56 = 46520226216352324323002797548303105981922548494168073941_<56>

Number: n N=1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473 ( 112 digits) SNFS difficulty: 155 digits. Divisors found: Mon Dec 10 21:43:43 2007 prp56 factor: 42618868918024524866536599051397923694814520254443166653 Mon Dec 10 21:43:43 2007 prp56 factor: 46520226216352324323002797548303105981922548494168073941 Mon Dec 10 21:43:43 2007 elapsed time 01:00:47 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.01 hours. Scaled time: 31.77 units (timescale=1.323). Factorization parameters were as follows: name: KA_4_0_153_9 n: 1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473 skew: 1.86 deg: 5 c5: 2 c0: 45 m: 10000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1200000) Primes: RFBsize:203362, AFBsize:203302, largePrimes:6863368 encountered Relations: rels:6330906, finalFF:483438 Max relations in full relation-set: 28 Initial matrix: 406729 x 483438 with sparse part having weight 36996653. Pruned matrix : 344289 x 346386 with weight 21435247. Total sieving time: 23.83 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 24.01 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 9, 2007 (2nd)

By Yousuke Koide
(10¹¹⁷⁷-1)/9 is divisible by 15112598396753272691345143612337643317_<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 9, 2007

By Jo Yeong Uk / GGNFS
5·10¹⁵⁴-9 = 4(9)₁₅₃1_<155> = 20431 · 52699109 · 32997845429069_<14> · 307535008641326161_<18> · C112
C112 = P35 · P78
P35 = 29858758013316752254424575775237339_<35>
P78 = 153258730444147188544171970047926818140030968120876657797177159787574781970379_<78>

Number: 49991_154 N=4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481 ( 112 digits) SNFS difficulty: 155 digits. Divisors found: r1=29858758013316752254424575775237339 (pp35) r2=153258730444147188544171970047926818140030968120876657797177159787574781970379 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.32 hours. Scaled time: 34.73 units (timescale=2.128). Factorization parameters were as follows: n: 4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481 m: 10000000000000000000000000000000 c5: 1 c0: -18 skew: 1.78 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:5614449 encountered Relations: rels:5616644, finalFF:590726 Max relations in full relation-set: 28 Initial matrix: 433819 x 590726 with sparse part having weight 45178149. Pruned matrix : 324617 x 326850 with weight 28243374. Total sieving time: 15.65 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.55 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 16.32 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

4·10¹⁶⁶+9 = 4(0)₁₆₅9_<167> = 95273 · 8165188054910845523309_<22> · 14974400622659504557368769453_<29> · C112
C112 = P50 · P63
P50 = 16787178947577077116058498947766265186683375867777_<50>
P63 = 204548731765952768246248790510940164302339098214505480636361977_<63>

Number: 40009_166 N=3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129 ( 112 digits) Divisors found: r1=16787178947577077116058498947766265186683375867777 (pp50) r2=204548731765952768246248790510940164302339098214505480636361977 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.28 hours. Scaled time: 37.04 units (timescale=2.144). Factorization parameters were as follows: name: 40009_166 n: 3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129 skew: 32399.49 # norm 4.04e+15 c5: 43260 c4: -2582623147 c3: -129295358935911 c2: -427069562025293841 c1: 24893025188825634820574 c0: -213047928497871312783824304 # alpha -6.19 Y1: 8847912799 Y0: -2398488377529493938175 # Murphy_E 7.74e-10 # M 1450873548697470902964069406047257719289617562836590192062108198415984904995949699924035264821588859357326623899 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1400000, 2240001) Primes: RFBsize:203362, AFBsize:203291, largePrimes:7436972 encountered Relations: rels:7186524, finalFF:474824 Max relations in full relation-set: 28 Initial matrix: 406739 x 474824 with sparse part having weight 42851975. Pruned matrix : 354327 x 356424 with weight 28562696. Polynomial selection time: 0.94 hours. Total sieving time: 15.41 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.68 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 17.28 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007 (3rd)

By matsui / GMP-ECM
(37·10¹⁷⁸-1)/9 = 4(1)_178<179> = 7 · 137 · C176
C176 = P33 · C144
P33 = 256606801414902925624321820940911_<33>
C144 = [167059987357085613333034797110824057589025658340318711449285988164500386196628719375549643795216399404461119111310119558935462349796606422281239_<144>]

Dec 8, 2007 (2nd)

By Jo Yeong Uk / GGNFS
5·10¹⁶²-9 = 4(9)₁₆₁1_<163> = C163
C163 = P44 · P56 · P64
P44 = 68385977371361886229008858431010504877885471_<44>
P56 = 10358845079111018892823016494495871163939965326959587059_<56>
P64 = 7058161771042422170571387133040680162138563583374078964992316019_<64>

Number: 49991_162 N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 163 digits) SNFS difficulty: 164 digits. Divisors found: r1=68385977371361886229008858431010504877885471 (pp44) r2=10358845079111018892823016494495871163939965326959587059 (pp56) r3=7058161771042422170571387133040680162138563583374078964992316019 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 48.82 hours. Scaled time: 104.66 units (timescale=2.144). Factorization parameters were as follows: n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 500000000000000000000000000000000 c5: 4 c0: -225 skew: 2.24 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2500000, 5100001) Primes: RFBsize:348513, AFBsize:348286, largePrimes:6727746 encountered Relations: rels:6971731, finalFF:855302 Max relations in full relation-set: 28 Initial matrix: 696863 x 855302 with sparse part having weight 63866792. Pruned matrix : 578415 x 581963 with weight 45564381. Total sieving time: 46.21 hours. Total relation processing time: 0.12 hours. Matrix solve time: 2.42 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000 total time: 48.82 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

5·10¹⁵¹-9 = 4(9)₁₅₀1_<152> = 41 · 71 · 5849 · 301673 · 2377056670405894456247259031_<28> · C112
C112 = P34 · P78
P34 = 7216593624182899656979319751461431_<34>
P78 = 567463522224990994815587976391783657930851218965846028456860191438113244343673_<78>

Number: 49991_151 N=4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063 ( 112 digits) SNFS difficulty: 151 digits. Divisors found: r1=7216593624182899656979319751461431 (pp34) r2=567463522224990994815587976391783657930851218965846028456860191438113244343673 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.78 hours. Scaled time: 27.42 units (timescale=2.146). Factorization parameters were as follows: n: 4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063 m: 1000000000000000000000000000000 c5: 50 c0: -9 skew: 0.71 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:175768, largePrimes:5401564 encountered Relations: rels:5292212, finalFF:469027 Max relations in full relation-set: 28 Initial matrix: 352135 x 469027 with sparse part having weight 39728717. Pruned matrix : 293297 x 295121 with weight 22323023. Total sieving time: 12.29 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.38 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 12.78 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007

By Robert Backstrom / GMP-ECM
5·10¹⁵⁷-9 = 4(9)₁₅₆1_<158> = 23 · 47 · 32993 · C151
C151 = P41 · P110
P41 = 64414577002263313514982818321328963237311_<41>
P110 = 21763981302826500962913776820417810329105314486317929333032864905086682541577240814547337472885523445053489457_<110>

Dec 7, 2007 (4th)

By Jo Yeong Uk / GGNFS
5·10¹⁴⁸-9 = 4(9)₁₄₇1_<149> = 29 · 79² · 109 · 752100379 · C133
C133 = P34 · P99
P34 = 3528305141284807144178302848697901_<34>
P99 = 955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729_<99>

Number: 49991_148 N=3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829 ( 133 digits) SNFS difficulty: 150 digits. Divisors found: r1=3528305141284807144178302848697901 (pp34) r2=955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729 (pp99) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.19 hours. Scaled time: 21.63 units (timescale=2.123). Factorization parameters were as follows: n: 3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829 m: 1000000000000000000000000000000 c5: 1 c0: -180 skew: 2.83 type: snfs 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, 1575001) Primes: RFBsize:135072, AFBsize:134763, largePrimes:3725528 encountered Relations: rels:3800513, finalFF:378509 Max relations in full relation-set: 28 Initial matrix: 269899 x 378509 with sparse part having weight 33652982. Pruned matrix : 230441 x 231854 with weight 17271651. Total sieving time: 9.90 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.21 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 10.19 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (3rd)

By Jo Yeong Uk / GGNFS
8·10¹⁸⁶-7 = 7(9)₁₈₅3_<187> = C187
C187 = P59 · P129
P59 = 23673718891878340687652156651068165346397873316066209701723_<59>
P129 = 337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491_<129>

Number: 79993_186 N=7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 187 digits) SNFS difficulty: 187 digits. Divisors found: r1=23673718891878340687652156651068165346397873316066209701723 (pp59) r2=337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491 (pp129) Version: GGNFS-0.77.1-20050930-nocona Total time: 403.36 hours. Scaled time: 859.97 units (timescale=2.132). Factorization parameters were as follows: n: 7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 20000000000000000000000000000000000000 c5: 5 c0: -14 skew: 1.23 type: snfs Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [6000000, 12600001) Primes: RFBsize:788060, AFBsize:788254, largePrimes:11493077 encountered Relations: rels:12030057, finalFF:1799960 Max relations in full relation-set: 28 Initial matrix: 1576379 x 1799960 with sparse part having weight 101413617. Pruned matrix : 1375471 x 1383416 with weight 74538419. Total sieving time: 389.01 hours. Total relation processing time: 0.27 hours. Matrix solve time: 13.95 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000 total time: 403.36 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (2nd)

By Sinkiti Sibata / PFGW
5·10¹⁰⁸²⁰-9 and 5·10¹⁴⁵⁹²-9 are PRP.

Dec 7, 2007

By Yousuke Koide
(10¹⁰⁹³-1)/9 is divisible by 199506195135220536755902065305293_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 6, 2007 (5th)

By Jo Yeong Uk / GMP-ECM
5·10¹⁹⁹-9 = 4(9)₁₉₈1_<200> = C200
C200 = P34 · P167
P34 = 1224112416041742410052808832168959_<34>
P167 = 40845921783620723265274965609618243098936302659169196754666765677273901878095642440080026040452661066087357309697423682859960350348666458327845592281510888305426519049_<167>

Dec 6, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve
(16·10¹⁶²-7)/9 =

1(7)_162<163>

= 149 · 12918999672424547147_<20> · C141
C141 = P53 · P89
P53 = 42410911175907381021122531054551380413053150932223867_<53>
P89 = 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477_<89>

Number: n N=923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559 ( 141 digits) SNFS difficulty: 163 digits. Divisors found: Thu Dec 06 08:21:53 2007 prp53 factor: 42410911175907381021122531054551380413053150932223867 Thu Dec 06 08:21:53 2007 prp89 factor: 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477 Thu Dec 06 08:21:53 2007 elapsed time 02:06:15 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 67.27 hours. Scaled time: 88.59 units (timescale=1.317). Factorization parameters were as follows: name: KA_1_7_162 n: 923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559 skew: 0.67 deg: 5 c5: 50 c0: -7 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2600000) Primes: RFBsize:216816, AFBsize:217591, largePrimes:7393862 encountered Relations: rels:6850636, finalFF:494540 Max relations in full relation-set: 28 Initial matrix: 434472 x 494540 with sparse part having weight 50632783. Pruned matrix : Total sieving time: 67.01 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,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 67.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

4·10¹⁵²+9 = 4(0)₁₅₁9_<153> = 26713 · 1234873 · 1996467668952176494127953_<25> · C118
C118 = P41 · P78
P41 = 35974049014171230767387935670841612478177_<41>
P78 = 168835367899724431687288680957130059518243845115630566914418157002167566445961_<78>

Number: n N=6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097 ( 118 digits) SNFS difficulty: 152 digits. Divisors found: Thu Dec 06 16:08:51 2007 prp41 factor: 35974049014171230767387935670841612478177 Thu Dec 06 16:08:51 2007 prp78 factor: 168835367899724431687288680957130059518243845115630566914418157002167566445961 Thu Dec 06 16:08:51 2007 elapsed time 00:47:53 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 22.03 hours. Scaled time: 31.99 units (timescale=1.452). Factorization parameters were as follows: name: KA_4_0_151_9 n: 6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097 skew: 0.94 deg: 5 c5: 25 c0: 18 m: 2000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1200000) Primes: RFBsize:148933, AFBsize:148625, largePrimes:7017509 encountered Relations: rels:6462685, finalFF:361511 Max relations in full relation-set: 28 Initial matrix: 297622 x 361511 with sparse part having weight 34777349. Pruned matrix : 266133 x 267685 with weight 22914288. Total sieving time: 21.83 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 22.03 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(34·10¹⁶¹-7)/9 = 3(7)_161<162> = 197 · 9371 · 110183 · 694182710171_<12> · C139
C139 = P58 · P82
P58 = 2616862112205494779410765284481436663033222318232195981387_<58>
P82 = 1022386293766035950048848925429858897403553614981437089485799152210536157188516281_<82>

Number: n N=2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747 ( 139 digits) SNFS difficulty: 162 digits. Divisors found: Thu Dec 06 23:56:31 2007 prp58 factor: 2616862112205494779410765284481436663033222318232195981387 Thu Dec 06 23:56:31 2007 prp82 factor: 1022386293766035950048848925429858897403553614981437089485799152210536157188516281 Thu Dec 06 23:56:31 2007 elapsed time 02:44:21 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 69.26 hours. Scaled time: 83.04 units (timescale=1.199). Factorization parameters were as follows: name: KA_3_7_161 n: 2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747 type: snfs skew: 0.46 deg: 5 c5: 340 c0: -7 m: 100000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000001) Primes: RFBsize:230209, AFBsize:229397, largePrimes:7454855 encountered Relations: rels:6893700, finalFF:514080 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 68.95 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,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 69.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Dec 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS
5·10¹⁴³-9 = 4(9)₁₄₂1_<144> = 17 · C143
C143 = P60 · P84
P60 = 285720265191441664337755675562698371459936363289423581013937_<60>
P84 = 102939022145228428989427304065983196665834399279521532082685405829806319911074359479_<84>

Number: 49991_143 N=29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823 ( 143 digits) SNFS difficulty: 144 digits. Divisors found: r1=285720265191441664337755675562698371459936363289423581013937 (pp60) r2=102939022145228428989427304065983196665834399279521532082685405829806319911074359479 (pp84) Version: GGNFS-0.77.1-20060513-k8 Total time: 11.80 hours. Scaled time: 23.49 units (timescale=1.991). Factorization parameters were as follows: name: 49991_143 n: 29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823 m: 50000000000000000000000000000 c5: 8 c0: -45 skew: 1.41 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1950001) Primes: RFBsize:100021, AFBsize:99898, largePrimes:2740628 encountered Relations: rels:2726242, finalFF:266126 Max relations in full relation-set: 28 Initial matrix: 199984 x 266126 with sparse part having weight 25911863. Pruned matrix : 180593 x 181656 with weight 15619042. Total sieving time: 11.27 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.36 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 11.80 hours. --------- CPU info (if available) ----------

5·10¹³⁵-9 = 4(9)₁₃₄1_<136> = 7 · 23 · 79 · 17536644897128650802233_<23> · C110
C110 = P46 · P65
P46 = 1719936531432379284578110469620659745107108719_<46>
P65 = 13033411521941582112132234407177385128654436282436915981843640207_<65>

Number: 49991_135 N=22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833 ( 110 digits) SNFS difficulty: 135 digits. Divisors found: r1=1719936531432379284578110469620659745107108719 (pp46) r2=13033411521941582112132234407177385128654436282436915981843640207 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.81 hours. Scaled time: 11.61 units (timescale=2.000). Factorization parameters were as follows: name: 49991_135 n: 22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833 m: 1000000000000000000000000000 c5: 5 c0: -9 skew: 1.12 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:63763, largePrimes:1597471 encountered Relations: rels:1658522, finalFF:230632 Max relations in full relation-set: 28 Initial matrix: 142327 x 230632 with sparse part having weight 17325623. Pruned matrix : 115642 x 116417 with weight 7445126. Total sieving time: 5.63 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.81 hours. --------- CPU info (if available) ----------

5·10¹⁴²-9 = 4(9)₁₄₁1_<143> = 2339 · 7678802901535212851801_<22> · C118
C118 = P30 · P44 · P46
P30 = 117630389300918643864328074179_<30>
P44 = 13290764272933581140590846123083681578082559_<44>
P46 = 1780642654590329845797643787582718386220435529_<46>

Number: 49991_142 N=2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269 ( 118 digits) SNFS difficulty: 142 digits. Divisors found: r1=117630389300918643864328074179 (pp30) r2=13290764272933581140590846123083681578082559 (pp44) r3=1780642654590329845797643787582718386220435529 (pp46) Version: GGNFS-0.77.1-20060513-k8 Total time: 15.52 hours. Scaled time: 30.95 units (timescale=1.994). Factorization parameters were as follows: name: 49991_142 n: 2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269 m: 10000000000000000000000000000 c5: 500 c0: -9 skew: 0.45 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2350001) Primes: RFBsize:100021, AFBsize:99988, largePrimes:2795102 encountered Relations: rels:2767439, finalFF:225205 Max relations in full relation-set: 28 Initial matrix: 200076 x 225205 with sparse part having weight 24651803. Pruned matrix : 193526 x 194590 with weight 19788059. Total sieving time: 14.86 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.47 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 15.52 hours. --------- CPU info (if available) ----------

Dec 6, 2007 (2nd)

By Sinkiti Sibata / PFGW
(22·10¹¹⁴³¹-7)/3 and (22·10¹²⁹²⁷-7)/3 are PRP.

Dec 6, 2007

By Robert Backstrom / GGNFS, Msieve 1.30
9·10¹⁶¹+7 = 9(0)₁₆₀7_<162> = 32742491009_<11> · 15305913553837_<14> · C139
C139 = P61 · P78
P61 = 2871374186022696036738055549847702632759229312163023359543043_<61>
P78 = 625434371370412843235342091358846490870084281799111208724718685614180061274753_<78>

Number: n N=1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379 ( 139 digits) SNFS difficulty: 161 digits. Divisors found: Thu Dec 06 02:15:29 2007 prp61 factor: 2871374186022696036738055549847702632759229312163023359543043 Thu Dec 06 02:15:29 2007 prp78 factor: 625434371370412843235342091358846490870084281799111208724718685614180061274753 Thu Dec 06 02:15:29 2007 elapsed time 01:54:10 (Msieve 1.30) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 65.06 hours. Scaled time: 84.97 units (timescale=1.306). Factorization parameters were as follows: name: KA_9_0_160_7 n: 1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379 skew: 0.60 deg: 5 c5: 90 c0: 7 m: 100000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300001) Primes: RFBsize:230209, AFBsize:230767, largePrimes:7363359 encountered Relations: rels:6836918, finalFF:495414 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 64.81 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 65.06 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 5, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM
5·10¹⁵³-9 = 4(9)₁₅₂1_<154> = 7² · 31 · 233 · 367 · 190668767 · 15049933389679_<14> · C125
C125 = P36 · P89
P36 = 394436722224962502210435443374249441_<36>
P89 = 34009384186180731129927406696605787600972387399376193654041569409619395347174902797719823_<89>

Dec 5, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS
5·10¹²³-9 = 4(9)₁₂₂1_<124> = 7 · 31 · 103668634195146479_<18> · C105
C105 = P33 · P72
P33 = 529652772019323584350569475910017_<33>
P72 = 419634942345057429532843777824194673588852290057980851002408093562224161_<72>
5·10¹²⁴-9 = 4(9)₁₂₃1_<125> = 112834510063289823811_<21> · C105
C105 = P45 · P60
P45 = 449489779543195000651111258759942012797389869_<45>
P60 = 985844086264210902762592892891295128151928079697441377159249_<60>

Number: n N=443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381 ( 105 digits) SNFS difficulty: 125 digits. Divisors found: r1=449489779543195000651111258759942012797389869 (pp45) r2=985844086264210902762592892891295128151928079697441377159249 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.96 hours. Scaled time: 2.60 units (timescale=1.323). Factorization parameters were as follows: name: KA_4_9_123_1 n: 443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381 skew: 1.78 deg: 5 c5: 1 c0: -18 m: 10000000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 250001) Primes: RFBsize:63951, AFBsize:63888, largePrimes:4613515 encountered Relations: rels:4003172, finalFF:210650 Max relations in full relation-set: 48 Initial matrix: 127906 x 210650 with sparse part having weight 17161578. Pruned matrix : 98518 x 99221 with weight 4907911. Total sieving time: 1.71 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.10 hours. Total square root time: 0.06 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 1.96 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 5, 2007

By Sinkiti Sibata / GGNFS
5·10¹²⁸-9 = 4(9)₁₂₇1_<129> = 17981 · 3843931457165509_<16> · C109
C109 = P45 · P64
P45 = 942477006562110761447064968719904363145782491_<45>
P64 = 7675554588296651640866311850875593032012524032228064348193639269_<64>

Number: 49991_128 N=7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079 ( 109 digits) SNFS difficulty: 129 digits. Divisors found: r1=942477006562110761447064968719904363145782491 (pp45) r2=7675554588296651640866311850875593032012524032228064348193639269 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.04 hours. Scaled time: 6.11 units (timescale=2.010). Factorization parameters were as follows: name: 49991_128 n: 7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079 m: 50000000000000000000000000 c5: 8 c0: -45 skew: 1.41 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:63951, AFBsize:63928, largePrimes:1408145 encountered Relations: rels:1391646, finalFF:160862 Max relations in full relation-set: 28 Initial matrix: 127944 x 160862 with sparse part having weight 8338899. Pruned matrix : 116420 x 117123 with weight 4694100. Total sieving time: 2.90 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,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 3.04 hours. --------- CPU info (if available) ----------

5·10¹²⁹-9 = 4(9)₁₂₈1_<130> = 7 · 399271 · C124
C124 = P37 · P88
P37 = 1719378230348833617587044366277777273_<37>
P88 = 1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311_<88>

Number: 49991_129 N=1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903 ( 124 digits) SNFS difficulty: 130 digits. Divisors found: r1=1719378230348833617587044366277777273 (pp37) r2=1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311 (pp88) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.02 hours. Scaled time: 6.07 units (timescale=2.010). Factorization parameters were as follows: name: 49991_129 n: 1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903 m: 100000000000000000000000000 c5: 1 c0: -18 skew: 1.78 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:63951, AFBsize:63888, largePrimes:1400726 encountered Relations: rels:1379152, finalFF:155356 Max relations in full relation-set: 28 Initial matrix: 127906 x 155356 with sparse part having weight 8163928. Pruned matrix : 118614 x 119317 with weight 4886712. Total sieving time: 2.88 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,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 3.02 hours. --------- CPU info (if available) ----------

5·10¹³¹-9 = 4(9)₁₃₀1_<132> = 41 · 5547391 · C124
C124 = P60 · P64
P60 = 331708005539959846200945699830264904120183676134446346135329_<60>
P64 = 6627373043733457754101972925473022695394088807721914419175039809_<64>

Number: 49991_131 N=2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161 ( 124 digits) SNFS difficulty: 131 digits. Divisors found: r1=331708005539959846200945699830264904120183676134446346135329 (pp60) r2=6627373043733457754101972925473022695394088807721914419175039809 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.40 hours. Scaled time: 8.73 units (timescale=1.985). Factorization parameters were as follows: name: 49991_131 n: 2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161 m: 100000000000000000000000000 c5: 50 c0: -9 skew: 0.71 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:64058, largePrimes:1540929 encountered Relations: rels:1578173, finalFF:205413 Max relations in full relation-set: 28 Initial matrix: 128074 x 205413 with sparse part having weight 14981903. Pruned matrix : 107027 x 107731 with weight 6295031. Total sieving time: 4.24 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.05 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.40 hours. --------- CPU info (if available) ----------

5·10¹³³-9 = 4(9)₁₃₂1_<134> = 1388981393_<10> · C125
C125 = P46 · P79
P46 = 4580943858133272901234098370518760018593679951_<46>
P79 = 7858119105566310646465581070947787541968136461241464994014105774627915529998537_<79>

Number: 49991_133 N=35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687 ( 125 digits) SNFS difficulty: 134 digits. Divisors found: r1=4580943858133272901234098370518760018593679951 (pp46) r2=7858119105566310646465581070947787541968136461241464994014105774627915529998537 (pp79) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.68 hours. Scaled time: 9.29 units (timescale=1.985). Factorization parameters were as follows: name: 49991_133 n: 35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687 m: 500000000000000000000000000 c5: 8 c0: -45 skew: 1.41 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 925001) Primes: RFBsize:78498, AFBsize:63928, largePrimes:1457680 encountered Relations: rels:1439431, finalFF:160358 Max relations in full relation-set: 28 Initial matrix: 142491 x 160358 with sparse part having weight 10506246. Pruned matrix : 136383 x 137159 with weight 7567068. Total sieving time: 4.48 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 4.68 hours. --------- CPU info (if available) ----------

5·10¹³⁴-9 = 4(9)₁₃₃1_<135> = 19 · 4294946301634720547509_<22> · C112
C112 = P40 · P72
P40 = 7661951585715267309757814664269644345249_<40>
P72 = 799685573994862057768981025766325851378881906722550433228529476184746329_<72>

Number: 49991_134 N=6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921 ( 112 digits) SNFS difficulty: 135 digits. Divisors found: r1=7661951585715267309757814664269644345249 (pp40) r2=799685573994862057768981025766325851378881906722550433228529476184746329 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.82 hours. Scaled time: 11.55 units (timescale=1.986). Factorization parameters were as follows: name: 49991_134 n: 6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921 m: 1000000000000000000000000000 c5: 1 c0: -18 skew: 1.78 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:63888, largePrimes:1619441 encountered Relations: rels:1697010, finalFF:245323 Max relations in full relation-set: 28 Initial matrix: 142453 x 245323 with sparse part having weight 18456007. Pruned matrix : 112751 x 113527 with weight 7450413. Total sieving time: 5.64 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.82 hours. --------- CPU info (if available) ----------

Dec 4, 2007 (5th)

By Jo Yeong Uk / GGNFS
5·10¹¹⁸-9 = 4(9)₁₁₇1_<119> = C119
C119 = P60 · P60
P60 = 113451761893099661361741916560523265424931846016438394824059_<60>
P60 = 440715940992725025596348804318707127294139212236448645152949_<60>

Number: 49991_118 N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 119 digits) SNFS difficulty: 120 digits. Divisors found: r1=113451761893099661361741916560523265424931846016438394824059 (pp60) r2=440715940992725025596348804318707127294139212236448645152949 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.74 hours. Scaled time: 1.58 units (timescale=2.145). Factorization parameters were as follows: n: 49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 1000000000000000000000000 c5: 1 c0: -180 skew: 2.83 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [300000, 420001) Primes: RFBsize:49098, AFBsize:49121, largePrimes:1721640 encountered Relations: rels:1663175, finalFF:113797 Max relations in full relation-set: 28 Initial matrix: 98283 x 113797 with sparse part having weight 8423002. Pruned matrix : 92995 x 93550 with weight 5618322. Total sieving time: 0.68 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,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 0.74 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Dec 4, 2007 (4th)

By Robert Backstrom / GMP-ECM
5·10¹¹³-9 = 4(9)₁₁₂1_<114> = 23 · 263 · 200041 · 2035289 · C99
C99 = P30 · P69
P30 = 443952373522730358003023095039_<30>
P69 = 457303931730390724716183370178707280616570660476664818059347925723369_<69>

Dec 4, 2007 (3rd)

By matsui / GMP-ECM
(4·10¹⁸⁵-13)/9 = (4)₁₈₄3_<185> = 7 · 1451 · C181
C181 = P33 · C149
P33 = 164277524510786827843488693745099_<33>
C149 = [26636298892028694012587941153238062628591187075841112023861911522751253412947765247273184353075516238787560153594780836262462832930974948643067577301_<149>]

Dec 4, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve
4·10¹⁶¹+9 = 4(0)₁₆₀9_<162> = 4051 · 127235411 · 1969369859_<10> · C141
C141 = P40 · P102
P40 = 3315928709727846416041854024938819789689_<40>
P102 = 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619_<102>

Number: n N=394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491 ( 141 digits) SNFS difficulty: 161 digits. Divisors found: Tue Dec 04 13:47:12 2007 prp40 factor: 3315928709727846416041854024938819789689 Tue Dec 04 13:47:12 2007 prp102 factor: 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619 Tue Dec 04 13:47:12 2007 elapsed time 01:05:12 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.49 hours. Scaled time: 45.35 units (timescale=1.440). Factorization parameters were as follows: name: KA_4_0_160_9 n: 394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491 skew: 0.74 deg: 5 c5: 40 c0: 9 m: 100000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1700000) Primes: RFBsize:203362, AFBsize:203082, largePrimes:7092138 encountered Relations: rels:6575017, finalFF:473191 Max relations in full relation-set: 28 Initial matrix: 406511 x 473191 with sparse part having weight 37652625. Pruned matrix : 356677 x 358773 with weight 25275013. Total sieving time: 31.28 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,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 31.49 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Dec 4, 2007

The factor table of 499...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 3, 2007 (3rd)

By Yousuke Koide
(10¹⁰¹⁹-1)/9 is divisible by 1164875952920329463736875905335015089_<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 3, 2007 (2nd)

By Robert Backstrom / GMP-ECM
(64·10²³⁴+53)/9 = 7(1)₂₃₃7_<235> = 13 · 1181 · 7451 · 1471598307214747_<16> · 3052073285905649_<16> · 172548225862787861_<18> · 2699321912890730492306803_<25> · C155
C155 = P47 · P109
P47 = 26652891282185821045577962549160542412294508503_<47>
P109 = 1114899980065870331232905973592925067977812491581216317251152807767466063464285258166500582274270472922906037_<109>

Dec 3, 2007

By Jo Yeong Uk / GGNFS
(4·10¹⁸⁷-1)/3 = 1(3)_187<188> = 13² · 71 · 641 · 4354373 · C174
C174 = P52 · P122
P52 = 5361712371792973170896785910460906141853462256912209_<52>
P122 = 74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791_<122>

Number: 13333_187 N=398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319 ( 174 digits) SNFS difficulty: 187 digits. Divisors found: r1=5361712371792973170896785910460906141853462256912209 (pp52) r2=74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791 (pp122) Version: GGNFS-0.77.1-20050930-nocona Total time: 361.56 hours. Scaled time: 773.01 units (timescale=2.138). Factorization parameters were as follows: n: 398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319 m: 20000000000000000000000000000000000000 c5: 25 c0: -2 skew: 0.6 type: snfs Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [6000000, 11900001) Primes: RFBsize:788060, AFBsize:788149, largePrimes:11393019 encountered Relations: rels:11956011, finalFF:1824015 Max relations in full relation-set: 28 Initial matrix: 1576273 x 1824015 with sparse part having weight 91057329. Pruned matrix : 1349070 x 1357015 with weight 64635248. Total sieving time: 348.71 hours. Total relation processing time: 0.26 hours. Matrix solve time: 12.46 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000 total time: 361.56 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).

Jo Yeong Uk completed factorizations up to n=200 of 133...33. Congratulations!

Dec 2, 2007

By Sinkiti Sibata / PFGW
2·10¹³⁵⁶¹+9, 2·10¹⁵⁹⁵⁵+9, (23·10¹³⁰⁹²-11)/3, (17·10¹¹⁰⁴⁶+7)/3, (17·10¹⁵⁴⁴⁸+7)/3, (17·10¹⁶⁶²⁸+7)/3, (17·10¹⁶⁹¹⁸+7)/3 and (17·10¹⁸⁷³⁴+7)/3 are PRP.

Dec 1, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
4·10¹⁶⁰+9 = 4(0)₁₅₉9_<161> = 277 · 138637 · 247609 · 15173733529_<11> · C138
C138 = P62 · P76
P62 = 60797126856307127135595444344471160234256633836042739865882569_<62>
P76 = 4559940072470123498850798447077277366305328269178339465898539108054593612449_<76>

Number: n N=277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481 ( 138 digits) SNFS difficulty: 160 digits. Divisors found: Sat Dec 01 14:19:53 2007 prp62 factor: 60797126856307127135595444344471160234256633836042739865882569 Sat Dec 01 14:19:53 2007 prp76 factor: 4559940072470123498850798447077277366305328269178339465898539108054593612449 Sat Dec 01 14:19:53 2007 elapsed time 01:19:11 Version: GGNFS-0.77.1-20051202-athlon Total time: 27.74 hours. Scaled time: 40.22 units (timescale=1.450). Factorization parameters were as follows: name: KA_4_0_159_9 n: 277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481 skew: 1.18 deg: 5 c5: 4 c0: 9 m: 100000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1500000) Primes: RFBsize:203362, AFBsize:203477, largePrimes:7032527 encountered Relations: rels:6512477, finalFF:474011 Max relations in full relation-set: 28 Initial matrix: 406903 x 474011 with sparse part having weight 35734018. Pruned matrix : 354822 x 356920 with weight 23455777. Total sieving time: 27.55 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 27.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 3400+

4·10¹⁵¹+9 = 4(0)₁₅₀9_<152> = 7 · 131 · 197 · 1531 · 47933 · 2296496011_<10> · 1404598779340570579_<19> · C111
C111 = P31 · P81
P31 = 6104431168415592413869608635611_<31>
P81 = 153232696611883288817148088275635599149717352290249536018399392505789557880036813_<81>
4·10¹⁵⁷+9 = 4(0)₁₅₆9_<158> = 7 · 87972114341735599736283329579_<29> · C128
C128 = P53 · P76
P53 = 22156740177008454467142813185853133375535106690625343_<53>
P76 = 2931642819433829612544003364072511581602586787125479620745479951967818422771_<76>

Number: n N=64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453 ( 128 digits) SNFS difficulty: 157 digits. Divisors found: Sat Dec 01 21:40:37 2007 prp53 factor: 22156740177008454467142813185853133375535106690625343 Sat Dec 01 21:40:37 2007 prp76 factor: 2931642819433829612544003364072511581602586787125479620745479951967818422771 Sat Dec 01 21:40:37 2007 elapsed time 01:33:31 (Msieve 1.30) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 37.39 hours. Scaled time: 48.71 units (timescale=1.303). Factorization parameters were as follows: name: KA_4_0_156_9 n: 64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453 skew: 0.94 deg: 5 c5: 25 c0: 18 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1600001) Primes: RFBsize:216816, AFBsize:216551, largePrimes:7116928 encountered Relations: rels:6581195, finalFF:473861 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 37.16 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 37.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

4·10¹⁶²+9 = 4(0)₁₆₁9_<163> = 13 · C162
C162 = P77 · P86
P77 = 14484959608208348655122569360348676482871487639034491862149522347733039174529_<77>
P86 = 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317_<86>

Number: n N=307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693 ( 162 digits) SNFS difficulty: 162 digits. Divisors found: Sun Dec 02 00:56:26 2007 prp77 factor: 14484959608208348655122569360348676482871487639034491862149522347733039174529 Sun Dec 02 00:56:26 2007 prp86 factor: 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317 Sun Dec 02 00:56:26 2007 elapsed time 01:38:38 (Msieve 1.30) Version: GGNFS-0.77.1-20051202-athlon Total time: 57.08 hours. Scaled time: 75.52 units (timescale=1.323). Factorization parameters were as follows: name: KA_4_0_161_9 n: 307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693 skew: 0.94 deg: 5 c5: 25 c0: 18 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2800000) Primes: RFBsize:216816, AFBsize:216551, largePrimes:7515407 encountered Relations: rels:6986522, finalFF:507662 Max relations in full relation-set: 28 Initial matrix: 433431 x 507662 with sparse part having weight 54891344. Pruned matrix : 403528 x 405759 with weight 36508693. Total sieving time: 56.79 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 57.08 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Dec 1, 2007 (4th)

By Yousuke Koide
10¹⁴⁹⁷+1 is divisible by 7016092401376747085885131800303253_<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 1, 2007 (3rd)

By Robert Backstrom / GGNFS
4·10¹⁵⁵+9 = 4(0)₁₅₄9_<156> = 1975423 · 3095912878954409_<16> · C134
C134 = P65 · P70
P65 = 34448312105302906122201979845692525321041884536529688865372252369_<65>
P70 = 1898642540091341888277141518857734481586769553402869501770427156234223_<70>

Number: n N=65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287 ( 134 digits) SNFS difficulty: 155 digits. Divisors found: r1=34448312105302906122201979845692525321041884536529688865372252369 (pp65) r2=1898642540091341888277141518857734481586769553402869501770427156234223 (pp70) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.75 hours. Scaled time: 32.02 units (timescale=1.197). Factorization parameters were as follows: name: KA_4_0_154_9 n: 65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287 type: snfs skew: 1.17 deg: 5 c5: 4 c0: 9 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:6166954 encountered Relations: rels:5660881, finalFF:507771 Max relations in full relation-set: 28 Initial matrix: 433816 x 507771 with sparse part having weight 24265495. Pruned matrix : 362409 x 364642 with weight 13836447. Total sieving time: 24.20 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.29 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 26.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Dec 1, 2007 (2nd)

By Sinkiti Sibata / Msieve
4·10¹⁷²+9 = 4(0)₁₇₁9_<173> = 379417 · 2183353693_<10> · 369214042069_<12> · 10392906827609765461_<20> · 1432364659536702101368956541_<28> · C100
C100 = P45 · P56
P45 = 521485688834094616003641826229481656646415453_<45>
P56 = 16846429736694498814138730507079319979241737624177166277_<56>

Thu Nov 29 14:35:06 2007 Msieve v. 1.30 Thu Nov 29 14:35:06 2007 random seeds: 5e6160f2 130a07ab Thu Nov 29 14:35:06 2007 factoring 8785172015635305902166850873310561627369223602890592020277003775916249170381081979472941403203278481 (100 digits) Thu Nov 29 14:35:06 2007 commencing quadratic sieve (100-digit input) Thu Nov 29 14:35:07 2007 using multiplier of 1 Thu Nov 29 14:35:07 2007 using 64kb Pentium 4 sieve core Thu Nov 29 14:35:07 2007 sieve interval: 18 blocks of size 65536 Thu Nov 29 14:35:07 2007 processing polynomials in batches of 6 Thu Nov 29 14:35:07 2007 using a sieve bound of 2825051 (102331 primes) Thu Nov 29 14:35:07 2007 using large prime bound of 423757650 (28 bits) Thu Nov 29 14:35:07 2007 using double large prime bound of 3379182069851550 (43-52 bits) Thu Nov 29 14:35:07 2007 using trial factoring cutoff of 52 bits Thu Nov 29 14:35:07 2007 polynomial 'A' values have 13 factors Sat Dec 1 08:30:49 2007 102586 relations (23428 full + 79158 combined from 1560356 partial), need 102427 Sat Dec 1 08:30:56 2007 begin with 1583784 relations Sat Dec 1 08:30:59 2007 reduce to 275743 relations in 14 passes Sat Dec 1 08:30:59 2007 attempting to read 275743 relations Sat Dec 1 08:31:11 2007 recovered 275743 relations Sat Dec 1 08:31:11 2007 recovered 267629 polynomials Sat Dec 1 08:31:11 2007 attempting to build 102586 cycles Sat Dec 1 08:31:11 2007 found 102586 cycles in 5 passes Sat Dec 1 08:31:11 2007 distribution of cycle lengths: Sat Dec 1 08:31:11 2007 length 1 : 23428 Sat Dec 1 08:31:11 2007 length 2 : 17036 Sat Dec 1 08:31:11 2007 length 3 : 16856 Sat Dec 1 08:31:11 2007 length 4 : 14145 Sat Dec 1 08:31:11 2007 length 5 : 11048 Sat Dec 1 08:31:11 2007 length 6 : 7584 Sat Dec 1 08:31:11 2007 length 7 : 5024 Sat Dec 1 08:31:11 2007 length 9+: 7465 Sat Dec 1 08:31:11 2007 largest cycle: 20 relations Sat Dec 1 08:31:12 2007 matrix is 102331 x 102586 with weight 6915312 (avg 67.41/col) Sat Dec 1 08:31:15 2007 filtering completed in 3 passes Sat Dec 1 08:31:15 2007 matrix is 98799 x 98863 with weight 6691681 (avg 67.69/col) Sat Dec 1 08:31:16 2007 saving the first 48 matrix rows for later Sat Dec 1 08:31:16 2007 matrix is 98751 x 98863 with weight 5212412 (avg 52.72/col) Sat Dec 1 08:31:16 2007 matrix includes 64 packed rows Sat Dec 1 08:31:16 2007 using block size 21845 for processor cache size 512 kB Sat Dec 1 08:31:17 2007 commencing Lanczos iteration Sat Dec 1 08:32:59 2007 lanczos halted after 1563 iterations (dim = 98750) Sat Dec 1 08:32:59 2007 recovered 16 nontrivial dependencies Sat Dec 1 08:33:01 2007 prp45 factor: 521485688834094616003641826229481656646415453 Sat Dec 1 08:33:01 2007 prp56 factor: 16846429736694498814138730507079319979241737624177166277 Sat Dec 1 08:33:01 2007 elapsed time 41:57:55

Dec 1, 2007

By Sinitiki Sibata / PFGW
4·10¹⁹⁶⁷⁹-9 is PRP.