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STUDIO KAMADA

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News and updates, June 2005

Jun 30, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹³⁷-18·10⁶⁸-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777577777777777777777777777777777777777777777777777777777777777777777777_<137> = 3 · 884363 · 553505604161_<12> · 3799866671149_<13> · C106
C106 = P46 · P61
P46 = 3139584356142145225486413564783334191312242041_<46>
P61 = 4439572722040745954689283568061219008015925598950385086497757_<61>

Number: 77577_68 N=13938413066074526459550572217872702166758177181291534495675201749827826630037025580766549200053608187602037 ( 107 digits) Divisors found: r1=3139584356142145225486413564783334191312242041 (pp46) r2=4439572722040745954689283568061219008015925598950385086497757 (pp61) Version: GGNFS-0.77.1 Total time: 24.73 hours. Scaled time: 16.47 units (timescale=0.666). Factorization parameters were as follows: name: 77577_68 n: 13938413066074526459550572217872702166758177181291534495675201749827826630037025580766549200053608187602037 skew: 26153.90 # norm 7.56e+14 c5: 5160 c4: -1257012006 c3: 4533546271449 c2: 976361616744067814 c1: 7358141065657339478068 c0: -304290792462030617262216 # alpha -5.32 Y1: 18800850643 Y0: -306417823973357441825 # Murphy_E 1.34e-09 # M 8780830775051261192254256101566781879965777699126972178494282960650192075929371822912518153518254264739592 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2600001) Relations: rels:4745417, finalFF:509851 Initial matrix: 365625 x 509851 with sparse part having weight 42527875. Pruned matrix : 318993 x 320885 with weight 17837218. Total sieving time: 21.14 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.92 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 24.73 hours. --------- CPU info (if available) ----------

Jun 29, 2005 (5th)

By Samuel Chong / GGNFS-0.77.1
10¹⁶¹-3 = (9)₁₆₀7_<161> = C161
C161 = P70 · P92
P70 = 1832934247661461281400687301882801770474799900077065371833785212553683_<70>
P92 = 54557330753999730405854658459191838430800911789742566920056359690858206347228970175385246959_<92>

Number: 99997_161 N=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 161 digits) SNFS difficulty: 161 digits. Divisors found: r1=1832934247661461281400687301882801770474799900077065371833785212553683 (pp70) r2=54557330753999730405854658459191838430800911789742566920056359690858206347228970175385246959 (pp92) Version: GGNFS-0.77.1 Total time: 60.24 hours. Scaled time: 66.50 units (timescale=1.104). Factorization parameters were as follows: name: 99997_161 n: 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 100000000000000000000000000000000 c5: 10 c0: -3 type: snfs skew: 0.7 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:282917, largePrimes:7030172 encountered Relations: rels:7299800, finalFF:756318 Max relations in full relation-set: 20 Initial matrix: 566129 x 756318 with sparse part having weight 56526770. Pruned matrix : 506316 x 509210 with weight 28850611. Total sieving time: 52.95 hours. Total relation processing time: 0.23 hours. Matrix solve time: 6.89 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 60.24 hours. --------- CPU info (if available) ---------- dual Athlon MP 2600+ (2.0GHz Bartons), 3GB RAM total elapsed time: 32h51m31.406s

Jun 29, 2005 (4th)

By Patrick De Geest / Jun 23, 2005
(82·10⁴³⁸⁸⁰+71)/9 = 9(1)₄₃₈₇₉9_<43881> is PRP.
By Patrick De Geest / Jun 26, 2005
(83·10³⁷⁷⁸⁶+61)/9 = 9(2)₃₇₇₈₅9_<37787> is PRP.

Jun 29, 2005 (3rd)

By Samuel Chong / GMP-ECM 6.0.1
(52·10¹⁶⁵-7)/9 = 5(7)_165<166> = C166
C166 = P36 · P131
P36 = 313862789381081919213237110091137467_<36>
P131 = 18408610301244054879443279259036322031382779494497999913003479922425729679234475767694159477151224688418434556725166139285255188931_<131>

Jun 29, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹⁴³-36·10⁷¹-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777777377777777777777777777777777777777777777777777777777777777777777777777777_<143> = 11 · 102071 · 28754261 · 80205253763_<11> · 260823065549741_<15> · C105
C105 = P52 · P53
P52 = 4761533364231980885181395443753493341945745354531189_<52>
P53 = 24185920515192961128829497062761621587444827284965931_<53>

Number: 77377_71 N=115162067477754024562918087384556074401558244350589408628121212622470605598872704565867664652208341921959 ( 105 digits) Divisors found: r1=4761533364231980885181395443753493341945745354531189 (pp52) r2=24185920515192961128829497062761621587444827284965931 (pp53) Version: GGNFS-0.77.1 Total time: 17.06 hours. Scaled time: 10.19 units (timescale=0.597). Factorization parameters were as follows: name: 77377_71 n: 115162067477754024562918087384556074401558244350589408628121212622470605598872704565867664652208341921959 skew: 57212.05 # norm 2.28e+14 c5: 1200 c4: 70737284 c3: -4449365244275 c2: -414628910607682135 c1: 5334143461390647495891 c0: 377185919224996589423906979 # alpha -5.98 Y1: 38161745767 Y0: -157189813397099087098 # Murphy_E 2.00e-09 # M 41335342175943446713747996473584525357871536267380113466463065723278983495237115314914455851303348086074 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2150001) Relations: rels:4880913, finalFF:645857 Initial matrix: 366203 x 645857 with sparse part having weight 46801850. Pruned matrix : 266297 x 268192 with weight 11558815. Total sieving time: 14.82 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.66 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 17.06 hours. --------- CPU info (if available) ----------

Jun 29, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(10¹³⁹+18·10⁶⁹-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111113111111111111111111111111111111111111111111111111111111111111111111111_<139> = 3 · 14479 · 1369466309_<10> · C125
C125 = P34 · P45 · P46
P34 = 4184092094865800336916701845043237_<34>
P45 = 893293804598802393281431649437994473684771919_<45>
P46 = 4997476473310700634780909783179017146879542389_<46>

Number: 11311_69 N=18678685738298794174046969957192960070916336444334060987947992036477848302805534597394113440809379070205875036128435095867367 ( 125 digits) SNFS difficulty: 140 digits. Divisors found: r1=4184092094865800336916701845043237 (pp34) r2=893293804598802393281431649437994473684771919 (pp45) r3=4997476473310700634780909783179017146879542389 (pp46) Version: GGNFS-0.77.0 Total time: 147.72 hours. Scaled time: 98.09 units (timescale=0.664). Factorization parameters were as follows: n: 18678685738298794174046969957192960070916336444334060987947992036477848302805534597394113440809379070205875036128435095867367 m: 100000000000000000000000000000000000 c4: 1 c2: 18 c0: -10 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 19000001) Relations: rels:3237474, finalFF:160698 Initial matrix: 142026 x 160698 with sparse part having weight 24923450. Pruned matrix : 140878 x 141652 with weight 20807866. Total sieving time: 143.31 hours. Total relation processing time: 3.89 hours. Matrix solve time: 0.45 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,140,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 147.72 hours. --------- CPU info (if available) ----------

Jun 28, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹⁴⁵-36·10⁷²-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777777773777777777777777777777777777777777777777777777777777777777777777777777777_<145> = 3 · 33857 · 507060199 · 3766094209_<10> · 5935426430706088879_<19> · C103
C103 = P47 · P57
P47 = 59443464427074334729157629370808569275103035673_<47>
P57 = 113652517762689411836180240338141093896068762859504638971_<57>

Number: 77377_72 N=6755899396673862009459505046706354892272941224688720232306642587547168598726070408097424680947999012483 ( 103 digits) Divisors found: r1=59443464427074334729157629370808569275103035673 (pp47) r2=113652517762689411836180240338141093896068762859504638971 (pp57) Version: GGNFS-0.77.1 Total time: 15.72 hours. Scaled time: 9.37 units (timescale=0.596). Factorization parameters were as follows: name: 77377_72 n: 6755899396673862009459505046706354892272941224688720232306642587547168598726070408097424680947999012483 skew: 40431.19 # norm 2.35e+14 c5: 3420 c4: 74118908 c3: -13835575302323 c2: 3726605185089849 c1: 11625778199282227060071 c0: -72042042160946319937303365 # alpha -5.79 Y1: 19670678723 Y0: -72298768767220674274 # Murphy_E 2.12e-09 # M 4280733064584259016568351758730077648894595582757764707168292691492191195813666337574719453010791144127 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1150000, 1950001) Relations: rels:4455020, finalFF:454450 Initial matrix: 339213 x 454450 with sparse part having weight 32467197. Pruned matrix : 293588 x 295348 with weight 13619684. Total sieving time: 12.96 hours. Total relation processing time: 0.38 hours. Matrix solve time: 2.08 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 15.72 hours. --------- CPU info (if available) ----------

Jun 27, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10¹⁴⁹-6·10⁷⁴-1)/3 = 33333333333333333333333333333333333333333333333333333333333333333333333333133333333333333333333333333333333333333333333333333333333333333333333333333_<149> = 1645105959193_<13> · 549896263989365396087204809637734957_<36> · C101
C101 = P35 · P66
P35 = 59088507105035948455390819680301591_<35>
P66 = 623592787042734103807313228026615522730609051188413739373310403063_<66>

Number: 33133_74 N=36847166827823763228931277868889258433231567607583557023069093744296139031526987578002088737610173233 ( 101 digits) Divisors found: r1=59088507105035948455390819680301591 (pp35) r2=623592787042734103807313228026615522730609051188413739373310403063 (pp66) Version: GGNFS-0.77.1 Total time: 12.14 hours. Scaled time: 7.25 units (timescale=0.597). Factorization parameters were as follows: name: 33133_74 n: 36847166827823763228931277868889258433231567607583557023069093744296139031526987578002088737610173233 skew: 2061.15 # norm 3.94e+13 c5: 510600 c4: -64342220 c3: -897473158979 c2: 10537454224105978 c1: -7393730521069466568 c0: -7372732815319682194560 # alpha -5.43 Y1: 24084012007 Y0: -9368384053546856099 # Murphy_E 3.10e-09 # M 15436513662557387529294245143531416636201359402394397310204520111026845119130537766733719357288242835 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [900000, 1600001) Relations: rels:4228087, finalFF:487758 Initial matrix: 269868 x 487758 with sparse part having weight 39557090. Pruned matrix : 208691 x 210104 with weight 9874067. Polynomial selection time: 0.33 hours. Total sieving time: 10.27 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.99 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 12.14 hours. --------- CPU info (if available) ----------

Jun 27, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹³⁷+36·10⁶⁸-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111511111111111111111111111111111111111111111111111111111111111111111111_<137> = 3 · 19 · 71 · 337 · 17041 · C126
C126 = P48 · P79
P48 = 421441220072673151631405605916567018262009237257_<48>
P79 = 1134389761960460886881885376405743011940355015986793071521429235760879875030177_<79>

Number: 11511_68 N=478078605318565907109850453990751759110387649253025838582800077989769882303434166081105987077670852646915556998044155627704489 ( 126 digits) SNFS difficulty: 137 digits. Divisors found: r1=421441220072673151631405605916567018262009237257 (pp48) r2=1134389761960460886881885376405743011940355015986793071521429235760879875030177 (pp79) Version: GGNFS-0.77.1 Total time: 31.93 hours. Scaled time: 30.50 units (timescale=0.955). Factorization parameters were as follows: n: 478078605318565907109850453990751759110387649253025838582800077989769882303434166081105987077670852646915556998044155627704489 m: 10000000000000000000000000000000000 c4: 10 c2: 36 c0: -1 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 3775001) Relations: rels:1717393, finalFF:167714 Initial matrix: 142708 x 167714 with sparse part having weight 20985311. Pruned matrix : 140336 x 141113 with weight 15721069. Total sieving time: 31.44 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.33 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 31.93 hours. --------- CPU info (if available) ----------

Jun 26, 2005 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹³⁹+9·10⁶⁹-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777778777777777777777777777777777777777777777777777777777777777777777777777_<139> = 17 · 677 · 174799 · 10796089709966723892211355663_<29> · C102
C102 = P40 · P63
P40 = 1619431214291851515000749284302973001453_<40>
P63 = 221131191553095858102340548721362892234957240074748045127193473_<63>

Number: 77877_69 N=358106754054634044213737010315384421193531136375089526504295315148840154621966188339153429665041116269 ( 102 digits) Divisors found: r1=1619431214291851515000749284302973001453 (pp40) r2=221131191553095858102340548721362892234957240074748045127193473 (pp63) Version: GGNFS-0.77.1 Total time: 13.75 hours. Scaled time: 9.16 units (timescale=0.666). Factorization parameters were as follows: name: 77877_69 n: 358106754054634044213737010315384421193531136375089526504295315148840154621966188339153429665041116269 skew: 42781.62 # norm 8.30e+13 c5: 840 c4: -35969722 c3: -2811953398404 c2: 12278280375104019 c1: 3172243310071161156676 c0: 42538643512976530241454951 # alpha -5.61 Y1: 10846187899 Y0: -53204382058511610320 # Murphy_E 2.74e-09 # M 295627027199131448071231397144316424902116359664442363969762974700191693172407930679170263033594015990 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1150000, 1850001) Relations: rels:4610174, finalFF:531429 Initial matrix: 338852 x 531429 with sparse part having weight 39765774. Pruned matrix : 264693 x 266451 with weight 11933215. Polynomial selection time: 0.33 hours. Total sieving time: 11.53 hours. Total relation processing time: 0.32 hours. Matrix solve time: 1.33 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 13.75 hours. --------- CPU info (if available) ----------

Jun 26, 2005 (2nd)

By Wataru Sakai / GMP-ECM 6.0.1
(28·10¹⁶⁴-1)/9 = 3(1)_164<165> = 1737265539857_<13> · 252249696241091_<15> · C138
C138 = P29 · P110
P29 = 26106630115401509928704918723_<29>
P110 = 27193671615382449140729179756297345921271319139648222513354703536214203678797979436152365081608209288658796511_<110>
(28·10¹⁷⁰-1)/9 = 3(1)_170<171> = 19 · 194022611 · 5328187985291_<13> · C149
C149 = P27 · C122
P27 = 523160083277781738962657179_<27>
C122 = [30275786718939073262198283789978155876672082056701271284678851780538889561037058996711978385933115010226062811804230797911_<122>]
(28·10¹⁷⁴-1)/9 = 3(1)_174<175> = 3 · 2971 · 10799 · 451939 · 605286277 · 5324553890743_<13> · C140
C140 = P33 · P108
P33 = 168517515354625529559054637391101_<33>
P108 = 131685862319569826123767299065424365952891770022473676802466204675977540215100361667406077973313830273073557_<108>
(79·10¹⁸²-7)/9 = 8(7)_182<183> = 115987387 · 125687914650272813477483495359_<30> · C146
C146 = P30 · C117
P30 = 277453739305469829129656557217_<30>
C117 = [217014980556087308878927231813617367028075041392377799114208275145971398575415608280897569212675022064944352895246557_<117>]

Jun 26, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹⁴¹-18·10⁷⁰-7)/9 = 777777777777777777777777777777777777777777777777777777777777777777777757777777777777777777777777777777777777777777777777777777777777777777777_<141> = 233 · 11113 · 232007 · 2111792219969_<13> · 84353798525778169_<17> · C100
C100 = P39 · P62
P39 = 352953140580240685743783096160847197447_<39>
P62 = 20591800718093390918495913306836168292815036621125855831795577_<62>

Number: 77577_70 N=7267940733653517707296451012967115921766358184798910647895987149003799541521580764580071594260291919 ( 100 digits) Divisors found: r1=352953140580240685743783096160847197447 (pp39) r2=20591800718093390918495913306836168292815036621125855831795577 (pp62) Version: GGNFS-0.77.1 Total time: 10.63 hours. Scaled time: 6.35 units (timescale=0.597). Factorization parameters were as follows: name: 77577_70 n: 7267940733653517707296451012967115921766358184798910647895987149003799541521580764580071594260291919 skew: 6644.82 # norm 1.59e+14 c5: 123120 c4: -974480016 c3: -9144399786380 c2: -8942139643844767 c1: 17268803406231924610 c0: -204465531944783777912712 # alpha -6.28 Y1: 11687674721 Y0: -8999480637777053393 # Murphy_E 3.13e-09 # M 2714786103330676513410033898228265489317158329577837996874109066379092597344062163433877596636689516 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [900000, 1500001) Relations: rels:4129872, finalFF:475867 Initial matrix: 270228 x 475867 with sparse part having weight 36702839. Pruned matrix : 205040 x 206455 with weight 9063096. Polynomial selection time: 0.33 hours. Total sieving time: 8.95 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.86 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 10.63 hours. --------- CPU info (if available) ----------

Jun 25, 2005 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10¹⁵¹-5·10⁷⁵-1 = 9999999999999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999999999999_<151> = 7 · 293 · 9539 · 15683 · 54258411269768597_<17> · 427783759648005329_<18> · C106
C106 = P46 · P60
P46 = 3517062300547732144252876581838513053265293857_<46>
P60 = 399237126270832542031473445700832275264923599868927241797897_<60>

Number: 99499_75 N=1404141845786159730429740222071762294828945006292206142265896945850516241497742346324533224878476709618729 ( 106 digits) Divisors found: r1=3517062300547732144252876581838513053265293857 (pp46) r2=399237126270832542031473445700832275264923599868927241797897 (pp60) Version: GGNFS-0.77.1 Total time: 20.20 hours. Scaled time: 13.45 units (timescale=0.666). Factorization parameters were as follows: name: 99499_75 n: 1404141845786159730429740222071762294828945006292206142265896945850516241497742346324533224878476709618729 skew: 20417.01 # norm 3.32e+14 c5: 11400 c4: -311860810 c3: 12167755640755 c2: 169336099166944217 c1: -3517189059279253542489 c0: -20222946190198593400537881 # alpha -5.97 Y1: 31933474111 Y0: -165234863264426566960 # Murphy_E 1.71e-09 # M 442288634088352137625259821992219151505734991060703111706403952540384173456401162565088843827489791074009 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2300001) Relations: rels:4763016, finalFF:564391 Initial matrix: 366513 x 564391 with sparse part having weight 45649436. Pruned matrix : 296929 x 298825 with weight 15263831. Polynomial selection time: 0.50 hours. Total sieving time: 16.98 hours. Total relation processing time: 0.47 hours. Matrix solve time: 1.98 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 20.20 hours. --------- CPU info (if available) ----------

Jun 25, 2005 (2nd)

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹³⁵-36·10⁶⁷-7)/9 = 777777777777777777777777777777777777777777777777777777777777777777737777777777777777777777777777777777777777777777777777777777777777777_<135> = 11 · 17² · 67 · 72707 · 15985362517_<11> · C115
C115 = P53 · P63
P53 = 24134275568127256336038479726753542342790015428526783_<53>
P63 = 130183881963273175231533304158072486413518393051052112152990257_<63>

Number: 77377_67 N=3141893681830186390130089036773194660026081857624140780532314295921848830769954838208312142442422878159973662553231 ( 115 digits) SNFS difficulty: 136 digits. Divisors found: r1=24134275568127256336038479726753542342790015428526783 (pp53) r2=130183881963273175231533304158072486413518393051052112152990257 (pp63) Version: GGNFS-0.77.1 Total time: 37.79 hours. Scaled time: 19.31 units (timescale=0.511). Factorization parameters were as follows: n: 3141893681830186390130089036773194660026081857624140780532314295921848830769954838208312142442422878159973662553231 m: 10000000000000000000000000000000000 c4: 7 c2: -36 c0: -70 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4225001) Relations: rels:1763505, finalFF:160460 Initial matrix: 142552 x 160460 with sparse part having weight 19861054. Pruned matrix : 140766 x 141542 with weight 16130213. Total sieving time: 36.91 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.73 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 37.79 hours. --------- CPU info (if available) ----------

Jun 25, 2005

By Samuel Chong / GGNFS-0.77.1
(5·10¹⁶⁰-17)/3 = 1(6)₁₅₉1_<161> = C161
C161 = P73 · P88
P73 = 7882418625046493137079200109466142233457102918797363849268660188394441163_<73>
P88 = 2114410241256167881019929854171578797976297286873491215535819386209922986237183824564047_<88>

Number: 16661_160 N=16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 ( 161 digits) SNFS difficulty: 160 digits. Divisors found: r1=7882418625046493137079200109466142233457102918797363849268660188394441163 (pp73) r2=2114410241256167881019929854171578797976297286873491215535819386209922986237183824564047 (pp88) Version: GGNFS-0.77.1 Total time: 44.33 hours. Scaled time: 48.94 units (timescale=1.104). Factorization parameters were as follows: name: 16661_160 n: 16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 m: 100000000000000000000000000000000 c5: 5 c0: -17 type: snfs skew: 1.4 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [2000000, 3100001) Relations: rels:7740521, finalFF:1050646 Max relations in full relation-set: 24 Initial matrix: 565968 x 1050646 with sparse part having weight 83903736. Pruned matrix : 417609 x 420502 with weight 23392534. Total sieving time: 39.65 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.31 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 44.33 hours. --------- CPU info (if available) ---------- dual Athlon MP 2600+ (2.0GHz Bartons), 3GB RAM total elapsed time: 26h34m15.203s

Jun 24, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹⁵¹+18·10⁷⁵-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777777777779777777777777777777777777777777777777777777777777777777777777777777777777777_<151> = 3 · 3371 · 167747 · 943601 · 24185170832763180443818023037_<29> · C108
C108 = P48 · P61
P48 = 169346109874757417843904031977676871790741094379_<48>
P61 = 1186336752025393198584033912651226741202452028767265265831509_<61>

Number: 77977_75 N=200901513956955081270327293751799424826200226008456663010883334938513692421828631863588058922940782080987911 ( 108 digits) Divisors found: r1=169346109874757417843904031977676871790741094379 (pp48) r2=1186336752025393198584033912651226741202452028767265265831509 (pp61) Version: GGNFS-0.77.1 Total time: 23.62 hours. Scaled time: 15.73 units (timescale=0.666). Factorization parameters were as follows: name: 77977_75 n: 200901513956955081270327293751799424826200226008456663010883334938513692421828631863588058922940782080987911 skew: 13846.45 # norm 2.03e+14 c5: 23400 c4: 809845272 c3: -2641094002024 c2: -213525271454027953 c1: 564132403817719659842 c0: 2480299527894433387021947 # alpha -5.24 Y1: 144903312829 Y0: -386146713039942139214 # Murphy_E 1.47e-09 # M 98349779625979756049703595573081058560548083551952179451017366893202083963636831223866291457045693186532823 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2450001) Relations: rels:4474962, finalFF:414352 Initial matrix: 366187 x 414352 with sparse part having weight 32180827. Pruned matrix : 345910 x 347804 with weight 21662205. Polynomial selection time: 0.94 hours. Total sieving time: 18.59 hours. Total relation processing time: 0.36 hours. Matrix solve time: 3.41 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 23.62 hours. --------- CPU info (if available) ----------

Jun 24, 2005

By Wataru Sakai / GMP-ECM 6.0.1
(79·10¹⁵⁵-7)/9 = 8(7)_155<156> = 233 · 10433 · 1481882918251259_<16> · C135
C135 = P28 · C107
P28 = 5408053588527112006899636743_<28>
C107 = [45057238943389029641403277796867297413112395948019299563561301516711477073402428700617197619020871097375389_<107>]
(79·10¹⁶³-7)/9 = 8(7)_163<164> = 3 · 74843 · 38060733327077701_<17> · C143
C143 = P28 · P115
P28 = 1083398825202294831704209103_<28>
P115 = 9480835858431198174849223900216501761666793567184223673469931008775997377554534316342050879918045338480030893555971_<115>
(79·10¹⁷⁴-7)/9 = 8(7)_174<175> = 23 · 111847 · 2700199 · 11341333 · 28678103502931_<14> · 5767905468864376763_<19> · C123
C123 = P26 · P97
P26 = 73719021324300880388201021_<26>
P97 = 9137437277905360554319628040724189738408180401913813774870087386642308107897726771619334377416327_<97>
(79·10¹⁸²-7)/9 = 8(7)_182<183> = 115987387 · C175
C175 = P30 · C146
P30 = 125687914650272813477483495359_<30>
C146 = [60211617840590252087949989171340449444131975941613010385946043012464564059565044302335961986003621602364869851210827579943438660712327824992751869_<146>]
(79·10¹⁹¹-7)/9 = 8(7)_191<192> = 163 · 818566172909689_<15> · C175
C175 = P31 · P145
P31 = 2085333327995178647780613948737_<31>
P145 = 3154769981065663717423453824301089431621799766297681716683244043756090996193911841402129171004373985965188845124589593043288901552008988704958003_<145>
(79·10¹⁹⁸-7)/9 = 8(7)_198<199> = 1286209 · C193
C193 = P26 · C168
P26 = 47217478072347778516414417_<26>
C168 = [144534076007327483294015834553477161019199808201781278959371252262113722534800307802918300030512630351102520759280855616387259510287054700793882474466213738567899443809_<168>]
(28·10¹⁸⁶-1)/9 = 3(1)_186<187> = 3⁴ · 53 · 131 · 199 · 4067309 · C172
C172 = P27 · P145
P27 = 916625868678918833697444587_<27>
P145 = 7456430668834257789935629689706953845490417530837617773240220206737721146056877271697384437834443068299796703587179227184524836846837788764124001_<145>
(28·10¹⁸⁷-1)/9 = 3(1)_187<188> = 179 · 1858889 · 48572115197_<11> · C169
C169 = P27 · C142
P27 = 440201725980094243625218327_<27>
C142 = [4372907351289223229267778825845950022974115758147345589181819982954699556380698836382389471097593379123455797524271583494620312221578927889999_<142>]

Jun 23, 2005 (3rd)

By Kenichiro Yamaguchi / GGNFS-0.77.1, GMP-ECM 6.0
(10¹³⁵-6·10⁶⁷-1)/3 = 333333333333333333333333333333333333333333333333333333333333333333313333333333333333333333333333333333333333333333333333333333333333333_<135> = 2083 · 321323 · 114664909 · 647245309 · C109
C109 = P40 · P69
P40 = 9251834436414450825830648393219171960261_<40>
P69 = 725304492835519725799380775948829474578870894276745894551318459324057_<69>

Number: 33133_67 N=6710397083701779729142349441629579134917644441680414304107635663746250452060508983802785279082528965725298877 ( 109 digits) SNFS difficulty: 136 digits. Divisors found: r1=9251834436414450825830648393219171960261 (pp40) r2=725304492835519725799380775948829474578870894276745894551318459324057 (pp69) Version: GGNFS-0.77.1 Total time: 36.38 hours. Scaled time: 18.63 units (timescale=0.512). Factorization parameters were as follows: n: 6710397083701779729142349441629579134917644441680414304107635663746250452060508983802785279082528965725298877 m: 10000000000000000000000000000000000 c4: 1 c2: -6 c0: -10 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4075001) Relations: rels:1764008, finalFF:159951 Initial matrix: 142152 x 159951 with sparse part having weight 20310478. Pruned matrix : 140403 x 141177 with weight 16509283. Total sieving time: 35.54 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.70 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 36.38 hours. --------- CPU info (if available) ----------

(10¹⁴¹+36·10⁷⁰-1)/9 = 111111111111111111111111111111111111111111111111111111111111111111111151111111111111111111111111111111111111111111111111111111111111111111111_<141> = 23 · 941 · 16741 · 118251965119_<12> · C121
C121 = P30 · P91
P30 = 899184948562321468607927788999_<30>
P91 = 2884039734134237755177191008659240780879866778331898494027158997512479778098162515038302937_<91>

Jun 23, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10¹⁴¹+15·10⁷⁰-1)/3 = 333333333333333333333333333333333333333333333333333333333333333333333383333333333333333333333333333333333333333333333333333333333333333333333_<141> = 4796218403_<10> · 4871092716755507520521488122659_<31> · C101
C101 = P45 · P56
P45 = 410088344293830932028617665624544383991341829_<45>
P56 = 34791725834592404126743198643481717824252849248670997001_<56>

Number: 33833_70 N=14267681242632902152177306366085252051103423473492844666433028856134586465350584189623177369224854829 ( 101 digits) Divisors found: r1=410088344293830932028617665624544383991341829 (pp45) r2=34791725834592404126743198643481717824252849248670997001 (pp56) Version: GGNFS-0.77.1 Total time: 11.78 hours. Scaled time: 7.86 units (timescale=0.667). Factorization parameters were as follows: name: 33833_70 n: 14267681242632902152177306366085252051103423473492844666433028856134586465350584189623177369224854829 skew: 4550.09 # norm 2.02e+14 c5: 136620 c4: 2274727068 c3: 6251553728793 c2: 18111130590571063 c1: -117823739326202695257 c0: 77998512955209787799585 # alpha -6.15 Y1: 5724874627 Y0: -10087115709131999442 # Murphy_E 3.11e-09 # M 10545509366654402031879847064245549972665555353600098223002255672948515358606393081821442210908882037 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [900000, 1600001) Relations: rels:4031378, finalFF:410818 Initial matrix: 270514 x 410818 with sparse part having weight 32167846. Pruned matrix : 227406 x 228822 with weight 10938842. Polynomial selection time: 0.35 hours. Total sieving time: 9.81 hours. Total relation processing time: 0.35 hours. Matrix solve time: 1.07 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 11.78 hours. --------- CPU info (if available) ----------

Jun 23, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10¹³⁵-4·10⁶⁷-1 = 999999999999999999999999999999999999999999999999999999999999999999959999999999999999999999999999999999999999999999999999999999999999999_<135> = 7 · 199 · 776868191153854013968671748788920791_<36> · C96
C96 = P46 · P51
P46 = 4793208491666876855263351806795609063791229239_<46>
P51 = 192785880758047470136230491036835852228315194280607_<51>

Number: 99599_67 N=924062920722951092337151139218331456487917511128942688202089863029871990343024979764022829068073 ( 96 digits) Divisors found: r1=4793208491666876855263351806795609063791229239 (pp46) r2=192785880758047470136230491036835852228315194280607 (pp51) Version: GGNFS-0.77.1 Total time: 16.97 hours. Scaled time: 10.11 units (timescale=0.596). Factorization parameters were as follows: name: 99599_67 n: 924062920722951092337151139218331456487917511128942688202089863029871990343024979764022829068073 m: 12476103279229687596272 deg: 4 c4: 38140440 c3: 19204245495 c2: 1110840043842648582 c1: -1228880260873486718 c0: -1807720023387482217793719 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.250 # E(F1,F2) = 1.827654e-05 # GGNFS version 0.77.1 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1119393583. # 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 Sieved special-q in [600000, 1920001) Relations: rels:2029757, finalFF:208466 Initial matrix: 185873 x 208466 with sparse part having weight 21798430. Pruned matrix : 180086 x 181079 with weight 16867637. Polynomial selection time: 0.17 hours. Total sieving time: 15.16 hours. Total relation processing time: 0.28 hours. Matrix solve time: 1.26 hours. Time per square root: 0.10 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: 16.97 hours. --------- CPU info (if available) ----------

Jun 22, 2005 (3rd)

By Samuel Chong / GMP-ECM 6.0.1
(10¹⁶⁵+17)/9 = (1)₁₆₄3_<165> = C165
C165 = P39 · P42 · P85
P39 = 392969699434825172058725656086390773767_<39>
P42 = 111993188756365886853577743582861876119213_<42>
P85 = 2524682766072869954796262839242693272891413803764401705446617232172532105793639005003_<85>

Jun 22, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10¹⁵¹+63·10⁷⁵-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111111111118111111111111111111111111111111111111111111111111111111111111111111111111111_<151> = 317 · 226621 · 544031 · 66083711 · 21179257669_<11> · 3209121692237716133_<19> · C100
C100 = P40 · P61
P40 = 4275012957575822946139264624771833515353_<40>
P61 = 1480626951383711539346468832225704939396997616241389872569663_<61>

Number: 11811_75 N=6329699402501354882735536081773742734114882424106313872387063047939192886925373223865767700672536039 ( 100 digits) Divisors found: r1=4275012957575822946139264624771833515353 (pp40) r2=1480626951383711539346468832225704939396997616241389872569663 (pp61) Version: GGNFS-0.77.1 Total time: 10.51 hours. Scaled time: 7.00 units (timescale=0.666). Factorization parameters were as follows: name: 11811_75 n: 6329699402501354882735536081773742734114882424106313872387063047939192886925373223865767700672536039 skew: 14052.57 # norm 8.35e+13 c5: 11760 c4: -18831542 c3: -8407661837023 c2: 27703402906256100 c1: 648695911680263659976 c0: 1428862511036605250637360 # alpha -5.79 Y1: 4538224819 Y0: -14002165221965969653 # Murphy_E 3.34e-09 # M 6163038367697848901014003635137676956818102186607531755848034578477748423578243747962055261019178131 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [900000, 1500001) Relations: rels:4192995, finalFF:499837 Initial matrix: 270060 x 499837 with sparse part having weight 37923867. Pruned matrix : 199682 x 201096 with weight 8631624. Total sieving time: 9.21 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.80 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 10.51 hours. --------- CPU info (if available) ----------

Jun 22, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1, GGNFS-0.77.0, GMP-ECM 6.0, msieve 0.88
(10¹³⁵+27·10⁶⁷-1)/9 = 111111111111111111111111111111111111111111111111111111111111111111141111111111111111111111111111111111111111111111111111111111111111111_<135> = 3 · 43 · 47 · 1129 · 332518649210987_<15> · C113
C113 = P39 · P75
P39 = 331592363289251899675730190676028301829_<39>
P75 = 147216148957514532570301830992508374412275270603655466615305118535416845991_<75>

Number: 11411_67 N=48815750747164781210733193033741522989460097994089613327715561193663369421731621664134355683888570277934956617539 ( 113 digits) SNFS difficulty: 136 digits. Divisors found: r1=331592363289251899675730190676028301829 (pp39) r2=147216148957514532570301830992508374412275270603655466615305118535416845991 (pp75) Version: GGNFS-0.77.1 Total time: 34.19 hours. Scaled time: 17.50 units (timescale=0.512). Factorization parameters were as follows: n: 48815750747164781210733193033741522989460097994089613327715561193663369421731621664134355683888570277934956617539 m: 10000000000000000000000000000000000 c4: 1 c2: 27 c0: -10 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 3925001) Relations: rels:1740943, finalFF:163904 Initial matrix: 142455 x 163904 with sparse part having weight 20477588. Pruned matrix : 140378 x 141154 with weight 15960162. Total sieving time: 33.37 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.68 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 34.19 hours. --------- CPU info (if available) ----------

(10¹³⁹+27·10⁶⁹-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111114111111111111111111111111111111111111111111111111111111111111111111111_<139> = 19 · 193 · C135
C135 = P51 · P84
P51 = 458969205309706883462311407189939442568908790037727_<51>
P84 = 660181018289950526503265195915261314434343241524003356600318014477235944992007303779_<84>

Number: 11411_69 N=303002757325091658334090840226646062479168560433899948489531254734418901312001939217646880586613338181377450534799866678786776959670333 ( 135 digits) SNFS difficulty: 140 digits. Divisors found: r1=458969205309706883462311407189939442568908790037727 (pp51) r2=660181018289950526503265195915261314434343241524003356600318014477235944992007303779 (pp84) Version: GGNFS-0.77.0 Total time: 105.88 hours. Scaled time: 70.31 units (timescale=0.664). Factorization parameters were as follows: n: 303002757325091658334090840226646062479168560433899948489531254734418901312001939217646880586613338181377450534799866678786776959670333 m: 100000000000000000000000000000000000 c4: 1 c2: 27 c0: -10 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 13600001) Relations: rels:2781306, finalFF:160760 Initial matrix: 142455 x 160760 with sparse part having weight 24151731. Pruned matrix : 141051 x 141827 with weight 20142129. Total sieving time: 104.11 hours. Total relation processing time: 1.28 hours. Matrix solve time: 0.43 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,140,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 105.88 hours. --------- CPU info (if available) ----------

(10¹⁴⁵+63·10⁷²-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111111118111111111111111111111111111111111111111111111111111111111111111111111111_<145> = 29² · 27594667 · 31879662713_<11> · 2049991686221_<13> · C111
C111 = P30 · P41 · P42
P30 = 172611700167822112088799043051_<30>
P41 = 11930586995803733710783320728974898140249_<41>
P42 = 355744731831617320345646967221453595047219_<42>

Jun 21, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10¹⁴⁷-2·10⁷³-1 = 999999999999999999999999999999999999999999999999999999999999999999999999979999999999999999999999999999999999999999999999999999999999999999999999999_<147> = 11 · 79 · 5413 · 624835533695896517_<18> · 364226024782606601290393_<24> · C99
C99 = P45 · P55
P45 = 469193742913951833708341512136612121140630107_<45>
P55 = 1990917625212558203593236322683252097549924778395642201_<55>

Number: 99799_73 N=934126092406836543261982582105796335015126432024245162073851432590364960820851929663448772060345507 ( 99 digits) Divisors found: r1=469193742913951833708341512136612121140630107 (pp45) r2=1990917625212558203593236322683252097549924778395642201 (pp55) Version: GGNFS-0.77.1 Total time: 21.34 hours. Scaled time: 12.72 units (timescale=0.596). Factorization parameters were as follows: name: 99799_73 n: 934126092406836543261982582105796335015126432024245162073851432590364960820851929663448772060345507 m: 2625189263492199113 deg: 5 c5: 7492080 c4: 1337515694 c3: -220253052859479 c2: -32970669423909232 c1: 18849870306766471780 c0: 465432639242354972464 skew: 107.623 type: gnfs # adj. I(F,S) = 46.631 # E(F1,F2) = 2.310504e-03 # GGNFS version 0.77.1 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1119252564. # maxskew=1500.0 # These parameters should be manually set: rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 type: gnfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [900000, 2200001) Relations: rels:4011223, finalFF:329970 Initial matrix: 270323 x 329970 with sparse part having weight 31478392. Pruned matrix : 251943 x 253358 with weight 18834109. Polynomial selection time: 0.57 hours. Total sieving time: 18.11 hours. Total relation processing time: 0.55 hours. Matrix solve time: 1.89 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 21.34 hours. --------- CPU info (if available) ----------

Jun 20, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴⁵-2·10⁷²-1 = 9999999999999999999999999999999999999999999999999999999999999999999999997999999999999999999999999999999999999999999999999999999999999999999999999_<145>

= 7² · 43 · C142
C142 = P33 · P110
P33 = 333494405578599951508082591758373_<33>
P110 = 14231376601563902084598105879773330680524057902968345305670008783724452852536115763742510732038567091916804809_<110>

Number: 979_72 N=4746084480303749406739439962031324157570004746084480303749406739439962030374940673943996203132415757000474608448030374940673943996203132415757 ( 142 digits) SNFS difficulty: 145 digits. Divisors found: r1=333494405578599951508082591758373 (pp33) r2=14231376601563902084598105879773330680524057902968345305670008783724452852536115763742510732038567091916804809 (pp110) Version: GGNFS-0.77.1 Total time: 133.37 hours. Scaled time: 88.83 units (timescale=0.666). Factorization parameters were as follows: name: 979_72 n: 474608448030374940673943996203132415757000474608448030374940673943996203037494067394399620313241575700047460844803037494067394399620 3132415757 m: 1000000000000000000000000000000000000 c4: 10 c2: -2 c0: -1 skew: 2 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 16150001) Relations: rels:4671165, finalFF:224076 Initial matrix: 199802 x 224076 with sparse part having weight 35215044. Pruned matrix : 196560 x 197623 with weight 29642185. Total sieving time: 129.03 hours. Total relation processing time: 1.88 hours. Matrix solve time: 2.39 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,145,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 133.37 hours. --------- CPU info (if available) ----------

Jun 19, 2005 (2nd)

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹³³-4·10⁶⁶-1 = 9999999999999999999999999999999999999999999999999999999999999999995999999999999999999999999999999999999999999999999999999999999999999_<133> = 31 · 137 · 7487097543124525709_<19> · C111
C111 = P40 · P71
P40 = 8115887942020483700339664052724822716727_<40>
P71 = 38749687619167420472280512971306132884586542208501397825133375024471019_<71>

Number: 99599_66 N=314488122505461292879671976094673380968666017980658029490893650491710086845199482260127907636464602097658034813 ( 111 digits) SNFS difficulty: 133 digits. Divisors found: r1=8115887942020483700339664052724822716727 (pp40) r2=38749687619167420472280512971306132884586542208501397825133375024471019 (pp71) Version: GGNFS-0.77.1 Total time: 17.31 hours. Scaled time: 8.92 units (timescale=0.515). Factorization parameters were as follows: n: 314488122505461292879671976094673380968666017980658029490893650491710086845199482260127907636464602097658034813 m: 1000000000000000000000000000000000 c4: 10 c2: -4 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 2200001) Relations: rels:1525062, finalFF:153120 Initial matrix: 127839 x 153120 with sparse part having weight 17151520. Pruned matrix : 125304 x 126007 with weight 12135532. Total sieving time: 16.78 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.42 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 17.31 hours. --------- CPU info (if available) ----------

Jun 19, 2005

jasonp's SIQS implementation msieve 1.0 was released.
Quadratic Sieve Source Code (jasonp)

Jun 18, 2005 (3rd)

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹³³-5·10⁶⁶-1 = 9999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999_<133> = 47 · 73 · 829 · 6761 · 50506030969_<11> · C113
C113 = P51 · P62
P51 = 131323299422472148930024532895341746762555988587153_<51>
P62 = 78402297452355609333372855409892683866758653385085863058626413_<62>

Number: 99499_66 N=10296048383745421024561376170444650610292091750811585702005887128202389975444353604023827357653984040572718272189 ( 113 digits) SNFS difficulty: 133 digits. Divisors found: r1=131323299422472148930024532895341746762555988587153 (pp51) r2=78402297452355609333372855409892683866758653385085863058626413 (pp62) Version: GGNFS-0.77.1 Total time: 18.98 hours. Scaled time: 10.04 units (timescale=0.529). Factorization parameters were as follows: n: 10296048383745421024561376170444650610292091750811585702005887128202389975444353604023827357653984040572718272189 m: 1000000000000000000000000000000000 c4: 10 c2: -5 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 2450001) Relations: rels:1564415, finalFF:146100 Initial matrix: 127969 x 146100 with sparse part having weight 17258837. Pruned matrix : 126104 x 126807 with weight 13491526. Total sieving time: 18.42 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.46 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 18.98 hours. --------- CPU info (if available) ----------

Jun 18, 2005 (2nd)

By Kenichiro Yamaguchi / GMP-ECM 6.0
(10¹⁵¹-6·10⁷⁵-1)/3 = 3333333333333333333333333333333333333333333333333333333333333333333333333331333333333333333333333333333333333333333333333333333333333333333333333333333_<151>

= 3411719 · 1367564468672449529_<19> · C126
C126 = P30 · P97
P30 = 136186205419691511152381762567_<30>
P97 = 5245955029205056738452064982416906027584911995774032103739413097905785105699345110067479580185549_<97>

Jun 18, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹³³+45·10⁶⁶-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111116111111111111111111111111111111111111111111111111111111111111111111_<133> = 3 · 17 · 1741 · 121843 · 206197 · 93151601 · C109
C109 = P38 · P71
P38 = 82126757743495966723850217964403708639_<38>
P71 = 65107439502914542128868047516770487220133623571504393789439718324411409_<71>

Number: 11611_66 N=5347062911355182067317850414313628272751587444555896181283436861210857551786593304439312027915642766403462351 ( 109 digits) SNFS difficulty: 133 digits. Divisors found: r1=82126757743495966723850217964403708639 (pp38) r2=65107439502914542128868047516770487220133623571504393789439718324411409 (pp71) Version: GGNFS-0.77.1 Total time: 26.69 hours. Scaled time: 13.05 units (timescale=0.489). Factorization parameters were as follows: n: 5347062911355182067317850414313628272751587444555896181283436861210857551786593304439312027915642766403462351 m: 1000000000000000000000000000000000 c4: 10 c2: 45 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 3250001) Relations: rels:1741242, finalFF:145760 Initial matrix: 128105 x 145760 with sparse part having weight 19065191. Pruned matrix : 126315 x 127019 with weight 15293701. Total sieving time: 25.69 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.83 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 26.69 hours. --------- CPU info (if available) ----------

(10¹³³+63·10⁶⁶-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111118111111111111111111111111111111111111111111111111111111111111111111_<133> = 197759 · C127
C127 = P36 · P92
P36 = 396019314659061651581554906203926729_<36>
P92 = 14187467032567588459817376264714088126285697525200698406889689033176784521761952527073842801_<92>

Number: 11811_66 N=5618510970985447494734050592443889335560511082231964720245910988213487685066728245546908667171208951861159851693784409868127929 ( 127 digits) SNFS difficulty: 133 digits. Divisors found: r1=396019314659061651581554906203926729 (pp36) r2=14187467032567588459817376264714088126285697525200698406889689033176784521761952527073842801 (pp92) Version: GGNFS-0.77.1 Total time: 22.79 hours. Scaled time: 11.40 units (timescale=0.500). Factorization parameters were as follows: n: 5618510970985447494734050592443889335560511082231964720245910988213487685066728245546908667171208951861159851693784409868127929 m: 1000000000000000000000000000000000 c4: 10 c2: 63 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 2900001) Relations: rels:1670903, finalFF:149663 Initial matrix: 127595 x 149663 with sparse part having weight 18686273. Pruned matrix : 125471 x 126172 with weight 14133399. Total sieving time: 21.90 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.77 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 22.79 hours. --------- CPU info (if available) ----------

(10¹³³+6·10⁶⁶-1)/3 = 3333333333333333333333333333333333333333333333333333333333333333335333333333333333333333333333333333333333333333333333333333333333333_<133> = 2347 · 3299 · 665236259 · 4857693449317_<13> · C105
C105 = P45 · P60
P45 = 382754370924383984959075115125158011950131091_<45>
P60 = 348062442898497241099906585776506243077787356301089086819257_<60>

Number: 33533_66 N=133222421374018633445036267132297777880987508567292617948187809460625006845713817438019021165601373219387 ( 105 digits) SNFS difficulty: 133 digits. Divisors found: r1=382754370924383984959075115125158011950131091 (pp45) r2=348062442898497241099906585776506243077787356301089086819257 (pp60) Version: GGNFS-0.77.1 Total time: 19.51 hours. Scaled time: 9.33 units (timescale=0.478). Factorization parameters were as follows: n: 133222421374018633445036267132297777880987508567292617948187809460625006845713817438019021165601373219387 m: 1000000000000000000000000000000000 c4: 10 c2: 6 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 2500001) Relations: rels:1586273, finalFF:146265 Initial matrix: 127609 x 146265 with sparse part having weight 17690356. Pruned matrix : 125447 x 126149 with weight 13804026. Total sieving time: 18.63 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.77 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 19.51 hours. --------- CPU info (if available) ----------

Jun 16, 2005

By Wataru Sakai / GMP-ECM 6.0.1
(64·10²¹⁸+53)/9 = 7(1)₂₁₇7_<219> = 3 · 97 · 1189063 · C211
C211 = P36 · P176
P36 = 147855171751831253349724806756031159_<36>
P176 = 13899625209206719452266689137337415260247158225314828795695264116500577538568280157205216813917164312242868729226115248983024299005746787654425475727273955434558847898710484111_<176>

Jun 15, 2005 (2nd)

By Makoto Kamada / GGNFS-0.77.1 gnfs
(10¹⁵¹+15·10⁷⁵-1)/3 = 3333333333333333333333333333333333333333333333333333333333333333333333333338333333333333333333333333333333333333333333333333333333333333333333333333333_<151> = 12309198275401_<14> · 172106671835554626673000063095659_<33> · C106
C106 = P33 · P73
P33 = 180796577788983913476033549582953_<33>
P73 = 8702841337317158145154140979945685450708672292591206796298372882756012079_<73>

Number: 33833_75 N=1573443930827446372689026635213482110463063784004453956533964342474724679041538499190915825174503880489287 ( 106 digits) Divisors found: r1=180796577788983913476033549582953 (pp33) r2=8702841337317158145154140979945685450708672292591206796298372882756012079 (pp73) Version: GGNFS-0.77.1 Total time: 14.00 hours. Scaled time: 12.03 units (timescale=0.859). Factorization parameters were as follows: name: 33833_75 n: 1573443930827446372689026635213482110463063784004453956533964342474724679041538499190915825174503880489287 skew: 26835.40 # norm 8.84e+14 c5: 32400 c4: 545718690 c3: -59957662137174 c2: 177053209068922201 c1: 21457461955680775036278 c0: -117977289162991443359241340 # alpha -6.86 Y1: 208093605929 Y0: -137169966717657942903 # Murphy_E 1.74e-09 # M 1099431901685208804753203883261783164596230715929709106406232058505912280650126081584776517850710123787560 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2150001) Relations: rels:4402773, finalFF:444850 Initial matrix: 366823 x 444850 with sparse part having weight 31071633. Pruned matrix : 331769 x 333667 with weight 16381417. Polynomial selection time: 0.50 hours. Total sieving time: 10.83 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.28 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 14.00 hours. --------- CPU info (if available) ----------

Jun 15, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1, GGNFS-0.77.0, GMP-ECM 6.0
(10¹³³+18·10⁶⁶-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111113111111111111111111111111111111111111111111111111111111111111111111_<133> = 3³ · 11939 · 26523766451086123_<17> · C111
C111 = P37 · P74
P37 = 9334726029996629638747991841927534061_<37>
P74 = 13921595242630642337527890331543853920769032729565157899809032183338983129_<74>

Number: 11311_66 N=129954277490461501898569740299982637721262154720309083556129626220110992716308982330303455565220754050251856869 ( 111 digits) SNFS difficulty: 133 digits. Divisors found: r1=9334726029996629638747991841927534061 (pp37) r2=13921595242630642337527890331543853920769032729565157899809032183338983129 (pp74) Version: GGNFS-0.77.1 Total time: 18.64 hours. Scaled time: 8.91 units (timescale=0.478). Factorization parameters were as follows: n: 129954277490461501898569740299982637721262154720309083556129626220110992716308982330303455565220754050251856869 m: 1000000000000000000000000000000000 c4: 10 c2: 18 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 400000) Relations: rels:1534758, finalFF:145793 Initial matrix: 127704 x 145793 with sparse part having weight 16630836. Pruned matrix : 125843 x 126545 with weight 12930014. Total sieving time: 17.79 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.73 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 18.64 hours. --------- CPU info (if available) ----------

10¹⁴¹-5·10⁷⁰-1 = 999999999999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999999999999_<141> = 94199759 · C134
C134 = P62 · P72
P62 = 45991197802202921691212410956857205150918173681404816125050149_<62>
P72 = 230821090102296748368286382776743795682256488181171518047153819469404989_<72>

Number: 99499_70 N=10615738411814832774678330121842456093757097616353774323350445089779900073842014818742795297384996494523940342564995309595218815793361 ( 134 digits) SNFS difficulty: 141 digits. Divisors found: r1=45991197802202921691212410956857205150918173681404816125050149 (pp62) r2=230821090102296748368286382776743795682256488181171518047153819469404989 (pp72) Version: GGNFS-0.77.0 Total time: 49.67 hours. Scaled time: 33.08 units (timescale=0.666). Factorization parameters were as follows: n: 10615738411814832774678330121842456093757097616353774323350445089779900073842014818742795297384996494523940342564995309595218815793361 type: snfs m: 100000000000000000000000000000000000 c4: 10 c2: -5 c0: -1 skew: 1 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 5850001) Relations: rels:3120132, finalFF:235006 Initial matrix: 200325 x 235006 with sparse part having weight 32657448. Pruned matrix : 196328 x 197393 with weight 24975412. Total sieving time: 48.48 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.97 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,141,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 49.67 hours. --------- CPU info (if available) ----------

(10¹⁵¹+15·10⁷⁵-1)/3 = 3333333333333333333333333333333333333333333333333333333333333333333333333338333333333333333333333333333333333333333333333333333333333333333333333333333_<151> = 12309198275401_<14> · C138
C138 = P33 · C106
P33 = 172106671835554626673000063095659_<33>
C106 = [1573443930827446372689026635213482110463063784004453956533964342474724679041538499190915825174503880489287_<106>]

Jun 14, 2005 (2nd)

By Patrick Keller / GMP-ECM
10¹⁶⁰-3 = (9)₁₅₉7_<160> = 13 · 383 · C157
C157 = P35 · C122
P35 = 52771123082243438120761219452533939_<35>
C122 = [38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637_<122>]

Jun 14, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(10¹³¹+72·10⁶⁵-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111911111111111111111111111111111111111111111111111111111111111111111_<131> = 7 · 43 · 4954121 · 85469737850611_<14> · C107
C107 = P34 · P74
P34 = 1230727592846495882729200715541547_<34>
P74 = 70835355177759964699490320620695881186959903046346813983743027104356745723_<74>

Jun 13, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴³-2·10⁷¹-1 = 99999999999999999999999999999999999999999999999999999999999999999999999799999999999999999999999999999999999999999999999999999999999999999999999_<143> = 11 · 3420316723_<10> · 2689592284789_<13> · 388813191244537_<15> · C106
C106 = P44 · P62
P44 = 35851493023476203089118525408940305117995409_<44>
P62 = 70893481324272999965729006376984212264740636943886258399324859_<62>

Number: 979_71 N=2541637151107113953623598003361310381710168418705511140128203704600780699595071560156063742850017061572331 ( 106 digits) SNFS difficulty: 144 digits. Divisors found: r1=35851493023476203089118525408940305117995409 (pp44) r2=70893481324272999965729006376984212264740636943886258399324859 (pp62) Version: GGNFS-0.77.1 Total time: 134.64 hours. Scaled time: 89.54 units (timescale=0.665). Factorization parameters were as follows: name: 979_71 n: 2541637151107113953623598003361310381710168418705511140128203704600780699595071560156063742850017061572331 m: 1000000000000000000000000000000000000 c4: 1 c2: -2 c0: -10 skew: 2 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 16350001) Relations: rels:4721621, finalFF:224199 Initial matrix: 199561 x 224199 with sparse part having weight 35297191. Pruned matrix : 196371 x 197432 with weight 29645821. Total sieving time: 129.63 hours. Total relation processing time: 2.58 hours. Matrix solve time: 2.37 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,144,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 134.64 hours. --------- CPU info (if available) ----------

Jun 13, 2005

By Wataru Sakai / GMP-ECM 6.0.1
(64·10²⁰²+53)/9 = 7(1)₂₀₁7_<203> = 19 · 31 · 818287 · 5871400771_<10> · 42012020311282391_<17> · C168
C168 = P45 · P124
P45 = 414262356522265732594185716792549665295299883_<45>
P124 = 1443862225455375214388574781017889982382760095348505921318244823845160256575391921560376858209721365591185744334089652279113_<124>

Jun 12, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(7·10¹³¹-9·10⁶⁵-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777677777777777777777777777777777777777777777777777777777777777777777_<131> = 23430181 · 74475769173523_<14> · C110
C110 = P39 · P72
P39 = 281478789560806858905657716699014710967_<39>
P72 = 158350418321298062938651182777170100239832005553412269462756155532807337_<72>

Jun 11, 2005 (2nd)

By Patrick Keller / GMP-ECM
10¹⁸⁸-3 = (9)₁₈₇7_<188> = 330546084791304846847511_<24> · C165
C165 = P34 · C131
P34 = 3562247528919238271756225579280817_<34>
C131 = [84926629533934787347098461076879779993835578096771335069286037224593611629072092542412229917972168238434939842601618598076985764731_<131>]
10¹⁷³-3 = (9)₁₇₂7_<173> = 379 · 443 · 587 · 15166668857_<11> · 47348365966898498973654947_<26> · C130
C130 = P32 · P98
P32 = 35007558660244164081437512887499_<32>
P98 = 40361001768340277480175803085457851847516030385154257084426979718995820425855241290021507034719463_<98>
10¹⁷⁶-3 = (9)₁₇₅7_<176> = 1630871011403_<13> · 274954356330508669_<18> · C147
C147 = P34 · C113
P34 = 6165326947505579813146109111140967_<34>
C113 = [36171262684763804729310148527389239248018395875233064507433824238903582995595207747275554709544383072041835224613_<113>]

Jun 11, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
10¹²⁹-8·10⁶⁴-1 = 999999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999999_<129> = 13 · 355137916961_<12> · 8620582561926197_<16> · C101
C101 = P47 · P55
P47 = 17394065538852265094936421036067329135787440209_<47>
P55 = 1444514437885723676563046033646529294763844095412943391_<55>

Number: 99199_64 N=25125978804402617019237644455161878627703533121609959064723179872696218764222048022455380870114208719 ( 101 digits) SNFS difficulty: 129 digits. Divisors found: r1=17394065538852265094936421036067329135787440209 (pp47) r2=1444514437885723676563046033646529294763844095412943391 (pp55) Version: GGNFS-0.77.0 Total time: 9.29 hours. Scaled time: 4.31 units (timescale=0.464). Factorization parameters were as follows: n: 25125978804402617019237644455161878627703533121609959064723179872696218764222048022455380870114208719 m: 100000000000000000000000000000000 c4: 10 c2: -8 c0: -1 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1300001) Relations: rels:1343062, finalFF:146400 Initial matrix: 127676 x 146400 with sparse part having weight 11815575. Pruned matrix : 125060 x 125762 with weight 8495459. Total sieving time: 8.79 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.41 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,129,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 9.29 hours. --------- CPU info (if available) ----------

(10¹³¹+36·10⁶⁵-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111511111111111111111111111111111111111111111111111111111111111111111_<131> = 3³ · 35822616597460223_<17> · C113
C113 = P34 · P39 · P40
P34 = 3463774676480380599377313037027121_<34>
P39 = 447944509182035286828280572358113016049_<39>
P40 = 7403934554416997775323358565782275753179_<40>

Number: 11511_65 N=11487788241968689340130776832134924441428019779863485243117750832304657883327884605483628835179286604237872959291 ( 113 digits) SNFS difficulty: 132 digits. Divisors found: r1=3463774676480380599377313037027121 (pp34) r2=447944509182035286828280572358113016049 (pp39) r3=7403934554416997775323358565782275753179 (pp40) Version: GGNFS-0.77.0 Total time: 29.88 hours. Scaled time: 13.77 units (timescale=0.461). Factorization parameters were as follows: n: 11487788241968689340130776832134924441428019779863485243117750832304657883327884605483628835179286604237872959291 m: 1000000000000000000000000000000000 c4: 1 c2: 36 c0: -10 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 3550001) Relations: rels:1820801, finalFF:147499 Initial matrix: 128035 x 147499 with sparse part having weight 19613667. Pruned matrix : 126086 x 126790 with weight 15472562. Total sieving time: 28.95 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.77 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,132,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 29.88 hours. --------- CPU info (if available) ----------

(10¹⁴¹+12·10⁷⁰-1)/3 = 333333333333333333333333333333333333333333333333333333333333333333333373333333333333333333333333333333333333333333333333333333333333333333333_<141> = C141
C141 = P42 · P100
P42 = 200311877610642489279530769709399194453521_<42>
P100 = 1664071733086403198656808450987068467724401913778352054621573899139316031505755175689630352671770373_<100>

Number: 33733_70 N=333333333333333333333333333333333333333333333333333333333333333333333373333333333333333333333333333333333333333333333333333333333333333333333 ( 141 digits) SNFS difficulty: 141 digits. Divisors found: r1=200311877610642489279530769709399194453521 (pp42) r2=1664071733086403198656808450987068467724401913778352054621573899139316031505755175689630352671770373 (pp100) Version: GGNFS-0.77.0 Total time: 46.04 hours. Scaled time: 30.66 units (timescale=0.666). Factorization parameters were as follows: n: 333333333333333333333333333333333333333333333333333333333333333333333373333333333333333333333333333333333333333333333333333333333333333333333 type: snfs m: 100000000000000000000000000000000000 c4: 10 c2: 12 c0: -1 skew: 1 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 5350001) Relations: rels:3024687, finalFF:237683 Initial matrix: 199722 x 237683 with sparse part having weight 32230331. Pruned matrix : 195415 x 196477 with weight 23977961. Total sieving time: 44.88 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.94 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,141,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 46.04 hours. --------- CPU info (if available) ----------

Jun 9, 2005 (3rd)

By Patrick Keller / GMP-ECM
10¹⁹⁶-3 = (9)₁₉₅7_<196> = 13 · 23 · 769 · 13230939634531520926993_<23> · C169
C169 = P30 · C139
P30 = 925002610176773043912732992351_<30>
C139 = [3553602327402028893556119121731169668177136744575884432068937264628665391192256931521572516434709261481036470145815539584064245135671768409_<139>]
10¹⁸⁴-3 = (9)₁₈₃7_<184> = 13² · 71 · 682781111 · 21237789308365515286691_<23> · C149
C149 = P29 · P32 · P89
P29 = 59850981433891272224551448459_<29>
P32 = 35526514573141366935363086929873_<32>
P89 = 27029640058852148978865133701306270767865770018364227207516059812926505552026723332704229_<89>
10¹⁸⁶-3 = (9)₁₈₅7_<186> = C186
C186 = P31 · C156
P31 = 2794375354729699423195302414791_<31>
C156 = [357861730460591695334295972163707008646716815727382711793133213691689104359175453265821274899204460799312954283262817577846710943629938175631885534582999067_<156>]
10¹⁶⁵-3 = (9)₁₆₄7_<165> = 431 · 56725169383_<11> · C152
C152 = P31 · P121
P31 = 6697081516361988272236718453873_<31>
P121 = 6107470012775150366829754092015054516474407019707159078145089779525145974239872649362120407931411527628863447502994173893_<121>

Jun 9, 2005 (2nd)

By Patrick Keller / GMP-ECM
10¹⁹⁰-3 = (9)₁₈₉7_<190> = 13 · 83 · 4643 · 60176382186443_<14> · 24247727135706472746493_<23> · 15856958895942670619463887_<26> · C122
C122 = P29 · P94
P29 = 33133578244863317770306493209_<29>
P94 = 2603721449712924915210778259443446461003757003516119146794621306240164054740371466779177155953_<94>
10¹⁷⁰-3 = (9)₁₆₉7_<170> = C170
C170 = P29 · C142
P29 = 38817280012777264790994290797_<29>
C142 = [2576172260577855142848298542798072596718901873646661264007524216056015115292366099141617460574776708224208202201460542857840458968464605723601_<142>]
10¹⁹²-3 = (9)₁₉₁7_<192> = 3373 · 1103279 · 30864312787215673925304239_<26> · C157
C157 = P33 · C125
P33 = 728214226699773901950646153594957_<33>
C125 = [11955907219789388090396927468596102846705760576688639467787460136053127454112956393569754103555054189544180606793438498318517_<125>]

Jun 9, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(7·10¹²⁹-36·10⁶⁴-7)/9 = 777777777777777777777777777777777777777777777777777777777777777737777777777777777777777777777777777777777777777777777777777777777_<129> = 19 · 1511 · 9605209 · C118
C118 = P52 · P67
P52 = 1155085458264857585266897235557737528591882771994781_<52>
P67 = 2441836210773539912784657450229065206157326950101786073984835385257_<67>

Number: 77377_64 N=2820529498529077726842896203812445693193396455368434647369401615489798725369725785914995995923727056965474236528343717 ( 118 digits) SNFS difficulty: 129 digits. Divisors found: r1=1155085458264857585266897235557737528591882771994781 (pp52) r2=2441836210773539912784657450229065206157326950101786073984835385257 (pp67) Version: GGNFS-0.77.0 Total time: 12.67 hours. Scaled time: 5.87 units (timescale=0.463). Factorization parameters were as follows: n: 2820529498529077726842896203812445693193396455368434647369401615489798725369725785914995995923727056965474236528343717 m: 100000000000000000000000000000000 c4: 70 c2: -36 c0: -7 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1650001) Relations: rels:1425379, finalFF:147524 Initial matrix: 128326 x 147524 with sparse part having weight 14352688. Pruned matrix : 125920 x 126625 with weight 10649810. Total sieving time: 12.04 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.52 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,129,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 12.67 hours. --------- CPU info (if available) ----------

(7·10¹²⁹+9·10⁶⁴-7)/9 = 777777777777777777777777777777777777777777777777777777777777777787777777777777777777777777777777777777777777777777777777777777777_<129> = 13 · 199 · 47527 · 23171657182230449_<17> · C105
C105 = P38 · P67
P38 = 37119386704565155173903619705798504661_<38>
P67 = 7354629739257217030665179729307139819782167801514595066178110388257_<67>

Number: 77877_64 N=272999345360383835733402078463522430412780573580465174510215546558101877901304328609826050405380734165877 ( 105 digits) SNFS difficulty: 129 digits. Divisors found: r1=37119386704565155173903619705798504661 (pp38) r2=7354629739257217030665179729307139819782167801514595066178110388257 (pp67) Version: GGNFS-0.77.0 Total time: 11.30 hours. Scaled time: 5.20 units (timescale=0.460). Factorization parameters were as follows: n: 272999345360383835733402078463522430412780573580465174510215546558101877901304328609826050405380734165877 m: 100000000000000000000000000000000 c4: 70 c2: 9 c0: -7 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1500001) Relations: rels:1420198, finalFF:158526 Initial matrix: 127529 x 158526 with sparse part having weight 14556171. Pruned matrix : 124013 x 124714 with weight 9056737. Total sieving time: 10.76 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.43 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,129,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 11.30 hours. --------- CPU info (if available) ----------

(7·10¹³⁵-54·10⁶⁷-7)/9 = 777777777777777777777777777777777777777777777777777777777777777777717777777777777777777777777777777777777777777777777777777777777777777_<135> = 3 · C135
C135 = P37 · P98
P37 = 8609335615997087769295147065984241781_<37>
P98 = 30113735928417888896209552856994879338389993563417374885930712104650757947392219012502066601505839_<98>

Number: 77177_67 N=259259259259259259259259259259259259259259259259259259259259259259239259259259259259259259259259259259259259259259259259259259259259259 ( 135 digits) SNFS difficulty: 136 digits. Divisors found: r1=8609335615997087769295147065984241781 (pp37) r2=30113735928417888896209552856994879338389993563417374885930712104650757947392219012502066601505839 (pp98) Version: GGNFS-0.77.0 Total time: 39.03 hours. Scaled time: 25.96 units (timescale=0.665). Factorization parameters were as follows: n: 259259259259259259259259259259259259259259259259259259259259259259239259259259259259259259259259259259259259259259259259259259259259259 type: snfs m: 10000000000000000000000000000000000 c4: 7 c2: -54 c0: -70 skew: 1 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4825001) Relations: rels:1859071, finalFF:159520 Initial matrix: 142322 x 159520 with sparse part having weight 21080069. Pruned matrix : 140699 x 141474 with weight 17383565. Total sieving time: 38.52 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.37 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,136,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 39.03 hours. --------- CPU info (if available) ----------

Jun 8, 2005 (2nd)

By Patrick De Geest
(23·10³⁵⁴⁶⁰+1)/3 = 7(6)₃₅₄₅₉7_<35461> is PRP.

Jun 8, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(7·10¹²⁷+18·10⁶³-7)/9 = 7777777777777777777777777777777777777777777777777777777777777779777777777777777777777777777777777777777777777777777777777777777_<127> = 3⁴ · 47 · 307 · 479 · C119
C119 = P53 · P66
P53 = 30631312724444235160545468056330338717803991423558901_<53>
P66 = 453558338502367035792988320604203378441041457101622160922749407487_<66>

Number: 77977_63 N=13893087305445341048925261340766454185809264453199872033789614218575666284298934646766277478837935790738765550594891787 ( 119 digits) SNFS difficulty: 128 digits. Divisors found: r1=30631312724444235160545468056330338717803991423558901 (pp53) r2=453558338502367035792988320604203378441041457101622160922749407487 (pp66) Version: GGNFS-0.77.0 Total time: 10.44 hours. Scaled time: 4.88 units (timescale=0.467). Factorization parameters were as follows: n: 13893087305445341048925261340766454185809264453199872033789614218575666284298934646766277478837935790738765550594891787 m: 100000000000000000000000000000000 c4: 7 c2: 18 c0: -70 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1400001) Relations: rels:1368098, finalFF:149950 Initial matrix: 127779 x 149950 with sparse part having weight 12746454. Pruned matrix : 124860 x 125562 with weight 8766000. Total sieving time: 9.93 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.41 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,128,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 10.44 hours. --------- CPU info (if available) ----------

(7·10¹²⁹-54·10⁶⁴-7)/9 = 777777777777777777777777777777777777777777777777777777777777777717777777777777777777777777777777777777777777777777777777777777777_<129> = 3 · 239 · 313 · 1483 · C121
C121 = P51 · P70
P51 = 819258050104320640258922665017523576202239376194061_<51>
P70 2852529660156642180800542536179761829606560163797913118844620621882899_<70>

Number: 77177_64 N=2336957887244671088095507911334083067482589873231609235540989577299026381579397913694934679868703977009259361334241262839 ( 121 digits) SNFS difficulty: 129 digits. Divisors found: r1=819258050104320640258922665017523576202239376194061 (pp51) r2=2852529660156642180800542536179761829606560163797913118844620621882899 (pp70) Version: GGNFS-0.77.0 Total time: 11.35 hours. Scaled time: 5.27 units (timescale=0.464). Factorization parameters were as follows: n: 2336957887244671088095507911334083067482589873231609235540989577299026381579397913694934679868703977009259361334241262839 m: 100000000000000000000000000000000 c4: 70 c2: -54 c0: -7 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1500001) Relations: rels:1399530, finalFF:152818 Initial matrix: 128020 x 152818 with sparse part having weight 13877072. Pruned matrix : 124879 x 125583 with weight 9359137. Total sieving time: 10.79 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.45 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,129,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 11.35 hours. --------- CPU info (if available) ----------

Jun 7, 2005 (2nd)

By Makoto Kamada / GMP-ECM 6.0.1
(55·10¹⁷⁶-1)/9 = 6(1)_176<177> = 13² · 229 · 566862379 · 17219215952723_<14> · C151
C151 = P24 · P127
P24 = 779422317838387832571071_<24>
P127 = 2075554531348294889830930553233256268923715932872011145984533488782114391510180113128553636420840720194863555419433818464208973_<127>

Jun 7, 2005

By Wataru Sakai / GMP-ECM 6.0.1
(64·10²³²+53)/9 = 7(1)₂₃₁7_<233> = 29 · 31 · 25544394638150569_<17> · 21891861055037187204902189298063661_<35> · C180
C180 = P37 · C144
P37 = 1156244055915277149927645527883080159_<37>
C144 = [122334784589234392683295194652612149338189319179115868523072772347572950426690801931827228533310815015647306731512386262336087369965447853346893_<144>]
(64·10²²²+53)/9 = 7(1)₂₂₁7_<223> = 13² · 246803 · 4770541 · 13798085473433_<14> · C196
C196 = P33 · C164
P33 = 133768138077661809781256269946047_<33>
C164 = [19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141_<164>]

Jun 6, 2005 (3rd)

By Kenichiro Yamaguchi / GGNFS-0.77.0
(7·10¹²⁷-45·10⁶³-7)/9 = 7777777777777777777777777777777777777777777777777777777777777772777777777777777777777777777777777777777777777777777777777777777_<127> = 347 · 14879 · C121
C121 = P44 · P77
P44 = 81725313759064580459926606720379788176638261_<44>
P77 = 18432986941378272876589867076688241033356098954517364832256309192034177979689_<77>

Number: 77277_63 N=1506441641300879501519321717334002021257311918017207738539061933947828095295862663483082025510642289255862376828758280829 ( 121 digits) SNFS difficulty: 128 digits. Divisors found: r1=81725313759064580459926606720379788176638261 (pp44) r2=18432986941378272876589867076688241033356098954517364832256309192034177979689 (pp77) Version: GGNFS-0.77.0 Total time: 11.35 hours. Scaled time: 5.30 units (timescale=0.467). Factorization parameters were as follows: n: 1506441641300879501519321717334002021257311918017207738539061933947828095295862663483082025510642289255862376828758280829 m: 100000000000000000000000000000000 c4: 7 c2: -45 c0: -70 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1450001) Relations: rels:1389505, finalFF:153588 Initial matrix: 127798 x 153588 with sparse part having weight 13736900. Pruned matrix : 124704 x 125406 with weight 9065744. Total sieving time: 10.83 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.42 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,128,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 11.35 hours. --------- CPU info (if available) ----------

(7·10¹²⁷-9·10⁶³-7)/9 = 7777777777777777777777777777777777777777777777777777777777777776777777777777777777777777777777777777777777777777777777777777777_<127> = 3 · 499 · 6217261 · C117
C117 = P48 · P70
P48 = 713181490360387714741821527620115836086086347897_<48>
P70 = 1171748935652690342842549975717980454423586038390038934347362604423173_<70>

Number: 77677_63 N=835669652256983742388095383122039530657312474352999172652316222358429427543858949880937914363786422476409261886617181 ( 117 digits) SNFS difficulty: 128 digits. Divisors found: r1=713181490360387714741821527620115836086086347897 (pp48) r2=1171748935652690342842549975717980454423586038390038934347362604423173 (pp70) Version: GGNFS-0.77.0 Total time: 10.42 hours. Scaled time: 4.87 units (timescale=0.467). Factorization parameters were as follows: n: 835669652256983742388095383122039530657312474352999172652316222358429427543858949880937914363786422476409261886617181 m: 100000000000000000000000000000000 c4: 7 c2: -9 c0: -70 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1400001) Relations: rels:1378927, finalFF:151771 Initial matrix: 127527 x 151771 with sparse part having weight 13117428. Pruned matrix : 124438 x 125139 with weight 8778971. Total sieving time: 9.91 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.41 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,128,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 10.42 hours. --------- CPU info (if available) ----------

(10¹³⁹+63·10⁶⁹-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111118111111111111111111111111111111111111111111111111111111111111111111111_<139> = C139
C139 = P57 · P82
P57 = 467652694300191693736261084612152646516775813624373744143_<57>
P82 = 2375932234868887528151906009973851128781214167960123415164812510915805241727384777_<82>

Number: 11811_69 N=1111111111111111111111111111111111111111111111111111111111111111111118111111111111111111111111111111111111111111111111111111111111111111111 ( 139 digits) SNFS difficulty: 140 digits. Divisors found: r1=467652694300191693736261084612152646516775813624373744143 (pp57) r2=2375932234868887528151906009973851128781214167960123415164812510915805241727384777 (pp82) Version: GGNFS-0.77.0 Total time: 104.76 hours. Scaled time: 69.77 units (timescale=0.666). Factorization parameters were as follows: n: 1111111111111111111111111111111111111111111111111111111111111111111118111111111111111111111111111111111111111111111111111111111111111111111 m: 100000000000000000000000000000000000 c4: 1 c2: 63 c0: -10 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 13450001) Relations: rels:2762046, finalFF:159690 Initial matrix: 142405 x 159690 with sparse part having weight 23961681. Pruned matrix : 140864 x 141640 with weight 20171454. Total sieving time: 104.04 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.43 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,140,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 104.76 hours. --------- CPU info (if available) ----------

Jun 6, 2005 (2nd)

By Bruce Dodson / GMP-ECM
10³⁶²+1 = 1(0)₃₆₁1_<363> = 101 · 928417781 · 469968172441_<12> · 2136569912461_<13> · 15470952779187481_<17> · 3467369151629862044701_<22> · 314547891171506427278717744569_<30> · C260
C260 = P47 · P214
P47 = 22780106292572351730658730234738216404394547689_<47>
P214 = 2763057708101686443032907255670870301200401399657924257107762182149956480304265507465823191458543338192444247826866701172774820848970862394309509034525824920430145923354279701799097867258088089212682054699054590801_<214>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 6, 2005

By Tomoya Adachi / GGNFS-0.73.5-nu6
(7·10¹³¹-27·10⁶⁵-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777477777777777777777777777777777777777777777777777777777777777777777_<131> = C131
C131 = P64 · P68
P64 = 2329957521561874313076509630588577468145156433739855730454265377_<64>
P68 = 33381629088945736991421982152696814983525014160319979864132043781201_<68>

# (7*10^131-27*10^65-7)/9 P64 = 2329957521561874313076509630588577468145156433739855730454265377 P68 = 33381629088945736991421982152696814983525014160319979864132043781201 sieve range: 130->169*10^4 with 12siever, on Ath64 3200+ maxrelsinff: 19 latsieve: 278:50 (4.65h) procrels: 16:57 matsolve: 31:49 sqrt : 10:15 (5deps) ----------------- total : 337:51 (5.63h) # 7*10^131-27*10^65-7 n: 77777777777777777777777777777777777777777777777777777777777777777477777777777777777777777777777777777777777777777777777777777777777 m: 1000000000000000000000000000000000 c4: 7 c2: -27 c0: -70 skew: 1.5 rlim: 1720000 alim: 1650000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 q0: 1720000 qintsize: 10000

(7·10¹⁴⁹-27·10⁷⁴-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777777777477777777777777777777777777777777777777777777777777777777777777777777777777_<149> = 499 · 6521 · 18713 · 6818941 · C132
C132 = P37 · P95
P37 = 3554935765272149714852015404523879867_<37>
P95 = 52692484515080030103968291662915380368443323585405263535692294815978557940825988997011167138933_<95>

# (7*10^149-27*10^74-7)/9 P37 = 3554935765272149714852015404523879867 P95 = 52692484515080030103968291662915380368443323585405263535692294815978557940825988997011167138933 sieve range: 125->235*10^4 with 13 siever, on Ath64 3200+ (16%), Pen4 3.4CGHz (62%), Pen4 2.4AGHz (22%) maxrelsinff: 48 latsieve: 1881:12 (31.35h) procrels: 61:23 matsolve: 126:24 sqrt : 9:25 (2deps) ----------------- total : 2078:24 (34.64h) # 7*10^149-27*10^74-7 n: 187318397763706925489496815847839758402513445252289852932278615416975849395188720690201203856299281148291551563449197762190990561911 m: 10000000000000000000000000000000000000 c4: 70 c2: -27 c0: -7 skew: 0.8 rlim: 1950000 alim: 1800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 q0: 1950000 qintsize: 10000

Jun 5, 2005 (3rd)

By Kenichiro Yamaguchi / GGNFS-0.77.0
10¹²⁵-7·10⁶²-1 = 99999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999_<125> = 71 · 26144460523_<11> · C113
C113 = P30 · P32 · P52
P30 = 472286871059656343279061123671_<30>
P32 = 55356921844173914450279278756291_<32>
P52 = 2060554760283018418628476621621143873632350669384223_<52>

Number: 99299_62 N=53871859508682512074646120936835098683229656719794964681152215122436137607489527995062577692969086789420004154203 ( 113 digits) SNFS difficulty: 125 digits. Divisors found: r1=472286871059656343279061123671 (pp30) r2=55356921844173914450279278756291 (pp32) r3=2060554760283018418628476621621143873632350669384223 (pp52) Version: GGNFS-0.77.0 Total time: 6.20 hours. Scaled time: 3.15 units (timescale=0.509). Factorization parameters were as follows: n: 53871859508682512074646120936835098683229656719794964681152215122436137607489527995062577692969086789420004154203 m: 10000000000000000000000000000000 c4: 10 c2: -7 c0: -1 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1000001) Relations: rels:2081493, finalFF:156249 Initial matrix: 112617 x 156249 with sparse part having weight 15831289. Pruned matrix : 109326 x 109953 with weight 8067291. Total sieving time: 5.78 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.30 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,125,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 6.20 hours. --------- CPU info (if available) ----------

(10¹²⁷+6·10⁶³-1)/3 = 3333333333333333333333333333333333333333333333333333333333333335333333333333333333333333333333333333333333333333333333333333333_<127> = 240893977 · C119
C119 = P50 · P60
P50 = 17148521859053648456529543149900190796330362694433_<50>
P69 = 806911885145198528723082540871527824980437341465412948199217266210813_<69>

Number: 33533_63 N=13837346100742623935895804208227810250869548861046589526534045869205494221772648692388574469561492329604128430879504029 ( 119 digits) SNFS difficulty: 128 digits. Divisors found: r1=17148521859053648456529543149900190796330362694433 (pp50) r2=806911885145198528723082540871527824980437341465412948199217266210813 (pp69) Version: GGNFS-0.77.0 Total time: 8.50 hours. Scaled time: 4.34 units (timescale=0.511). Factorization parameters were as follows: n: 13837346100742623935895804208227810250869548861046589526534045869205494221772648692388574469561492329604128430879504029 m: 100000000000000000000000000000000 c4: 1 c2: 6 c0: -10 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1300001) Relations: rels:1384878, finalFF:160526 Initial matrix: 127835 x 160526 with sparse part having weight 12651030. Pruned matrix : 123784 x 124487 with weight 7412218. Total sieving time: 8.08 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.34 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 8.50 hours. --------- CPU info (if available) ----------

(7·10¹²⁷-27·10⁶³-7)/9 = 7777777777777777777777777777777777777777777777777777777777777774777777777777777777777777777777777777777777777777777777777777777_<127> = 1311131228976887739433_<22> · C106
C106 = P49 · P58
P49 = 4522206285626725741274186571771733389102946815497_<49>
P58 = 1311773942191118801724309113945969200258141511100574341377_<58>

Number: 77477_63 N=5932112366698026612643230407147817616017134496767110825184794419449538664238789943499702740785470311919369 ( 106 digits) SNFS difficulty: 128 digits. Divisors found: r1=4522206285626725741274186571771733389102946815497 (pp49) r2=1311773942191118801724309113945969200258141511100574341377 (pp58) Version: GGNFS-0.77.0 Total time: 9.99 hours. Scaled time: 4.76 units (timescale=0.476). Factorization parameters were as follows: n: 5932112366698026612643230407147817616017134496767110825184794419449538664238789943499702740785470311919369 m: 100000000000000000000000000000000 c4: 7 c2: -27 c0: -70 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1350001) Relations: rels:1375961, finalFF:156458 Initial matrix: 127414 x 156458 with sparse part having weight 12906960. Pruned matrix : 123672 x 124373 with weight 8006852. Total sieving time: 9.49 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.39 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 9.99 hours. --------- CPU info (if available) ----------

(7·10¹²⁷-18·10⁶³-7)/9 = 7777777777777777777777777777777777777777777777777777777777777775777777777777777777777777777777777777777777777777777777777777777_<127> = C127
C127 = P40 · P42 · P47
P40 = 5524802449290085157573703075130787287549_<40>
P42 = 116659172373616594305474819802771926786157_<42>
P47 = 12067571647473808661607754552473705721153447289_<47>

Number: 77577_63 N=7777777777777777777777777777777777777777777777777777777777777775777777777777777777777777777777777777777777777777777777777777777 ( 127 digits) SNFS difficulty: 128 digits. Divisors found: r1=5524802449290085157573703075130787287549 (pp40) r2=116659172373616594305474819802771926786157 (pp42) r3=12067571647473808661607754552473705721153447289 (pp47) Version: GGNFS-0.77.0 Total time: 14.69 hours. Scaled time: 7.52 units (timescale=0.512). Factorization parameters were as follows: n: 7777777777777777777777777777777777777777777777777777777777777775777777777777777777777777777777777777777777777777777777777777777 m: 100000000000000000000000000000000 c4: 7 c2: -18 c0: -70 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 2000001) Relations: rels:1532950, finalFF:150473 Initial matrix: 127501 x 150473 with sparse part having weight 16717144. Pruned matrix : 125244 x 125945 with weight 12107412. Total sieving time: 14.03 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.54 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,4,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 14.69 hours. --------- CPU info (if available) ----------

Jun 5, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴¹-2·10⁷⁰-1 = 999999999999999999999999999999999999999999999999999999999999999999999979999999999999999999999999999999999999999999999999999999999999999999999_<141> = 151 · 29952681391_<11> · 26707653448326308357669563_<26> · C103
C103 = P33 · P71
P33 = 776542093594587270889336430100377_<33>
P71 = 10660721824502037370806767990901105962219062345005297373975234579520189_<71>

Number: 979_70 N=8278499244828320278031558513661543374807561301980190150664926388700788596726190851264578119573768011253 ( 103 digits) SNFS difficulty: 141 digits. Divisors found: r1=776542093594587270889336430100377 (pp33) r2=10660721824502037370806767990901105962219062345005297373975234579520189 (pp71) Version: GGNFS-0.77.1 Total time: 46.66 hours. Scaled time: 27.81 units (timescale=0.596). Factorization parameters were as follows: name: 979_70 n: 8278499244828320278031558513661543374807561301980190150664926388700788596726190851264578119573768011253 m: 100000000000000000000000000000000000 c4: 10 c2: -2 c0: -1 skew: 2 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 5550001) Relations: rels:3063360, finalFF:234257 Initial matrix: 199802 x 234257 with sparse part having weight 32040517. Pruned matrix : 195862 x 196925 with weight 24490361. Total sieving time: 43.91 hours. Total relation processing time: 0.71 hours. Matrix solve time: 1.96 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,141,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 46.66 hours. --------- CPU info (if available) ----------

Jun 5, 2005

By Makoto Kamada / GMP-ECM 6.0
10¹³⁵-4·10⁶⁷-1 = 999999999999999999999999999999999999999999999999999999999999999999959999999999999999999999999999999999999999999999999999999999999999999_<135> = 7 · 199 · C132
C132 = P36 · C96
P36 = 776868191153854013968671748788920791_<36>
C96 = [924062920722951092337151139218331456487917511128942688202089863029871990343024979764022829068073_<96>]

Jun 3, 2005 (4th)

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴⁹-10⁷⁴-1 = 99999999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999999_<149> = 61 · 18917 · 44457307 · 2986416743_<10> · 34754472743_<11> · C116
C116 = P44 · P72
P44 = 34517731760870911581764325642423398651167757_<44>
P72 = 544090801698841188467997932847833144106032723664810376251870210457031777_<72>

Number: 989_74 N=18780780346597807427108915807137709206674619173761487048601495290033742608032378270882237240993404172741573106814189 ( 116 digits) SNFS difficulty: 150 digits. Divisors found: r1=34517731760870911581764325642423398651167757 (pp44) r2=544090801698841188467997932847833144106032723664810376251870210457031777 (pp72) Version: GGNFS-0.77.1 Total time: 64.30 hours. Scaled time: 42.82 units (timescale=0.666). Factorization parameters were as follows: name: 989_74 n: 18780780346597807427108915807137709206674619173761487048601495290033742608032378270882237240993404172741573106814189 m: 10000000000000000000000000 c6: 1 c3: -1 c0: -10 skew: 2 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [750000, 2550001) Relations: rels:2975533, finalFF:284922 Initial matrix: 228217 x 284922 with sparse part having weight 31497873. Pruned matrix : 220442 x 221647 with weight 19729500. Total sieving time: 61.82 hours. Total relation processing time: 0.31 hours. Matrix solve time: 2.02 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,150,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 64.30 hours. --------- CPU info (if available) ----------

Jun 3, 2005 (3rd)

By Makoto Kamada / PFGW 1.2
(2·10¹⁹¹⁵³+691)/9 = (2)₁₉₁₅₁99_<19153> is PRP.
I was surprized that this 19153 digit number is the smallest prime or PRP of the form 22...2299.

Jun 3, 2005 (2nd)

By Makoto Kamada / GMP-ECM 6.0.1
(5·10¹⁵⁵-41)/9 = (5)₁₅₄1_<155> = 3 · 67 · 32728614939259_<14> · C139
C139 = P36 · P104
P36 = 192515053023680624529300156089570641_<36>
P104 = 43867119492678689661734121972076445309646265049947481084645349682018075487964108144385723980490281754229_<104>
(7·10¹³¹-18·10⁶⁵-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777577777777777777777777777777777777777777777777777777777777777777777_<131> = 3 · 109 · 823 · 81331 · 82320101 · 9514718303_<10> · C103
C103 = P30 · P74
P30 = 341218957060259517352733160503_<30>
P74 = 13295872745065450636615972105518984032973924478911738099361722222461180503_<74>

Jun 3, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
10¹¹¹-8·10⁵⁵-1 = 999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999_<111> = 79 · C110
C110 = P34 · P76
P34 = 5016332105457035533508494815374477_<34>
P76 = 2523403072601785194850307494500371919914170316323356023807466059956538685653_<76>

Number: 99199_55 N=12658227848101265822784810126582278481012658227848101264810126582278481012658227848101265822784810126582278481 ( 110 digits) SNFS difficulty: 112 digits. Divisors found: r1=5016332105457035533508494815374477 (pp34) r2=2523403072601785194850307494500371919914170316323356023807466059956538685653 (pp76) Version: GGNFS-0.77.0 Total time: 1.67 hours. Scaled time: 0.87 units (timescale=0.520). Factorization parameters were as follows: n: 12658227848101265822784810126582278481012658227848101264810126582278481012658227848101265822784810126582278481 m: 10000000000000000000000000000 c4: 1 c2: -8 c0: -10 skew: 1 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [250000, 430001) Relations: rels:994974, finalFF:105148 Initial matrix: 79232 x 105148 with sparse part having weight 4446466. Pruned matrix : 72703 x 73163 with weight 2092781. Total sieving time: 1.58 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,112,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 1.67 hours. --------- CPU info (if available) ----------

(10¹²¹+72·10⁶⁰-1)/9 = 1111111111111111111111111111111111111111111111111111111111119111111111111111111111111111111111111111111111111111111111111_<121> = 3 · 39499 · 4366643 · 113400914609_<12> · C98
C98 = P44 · P55
P44 = 18603945024252359647586172479299347296895947_<44>
P55 = 1017843114992066265791411519193442648002770541494100167_<55>

Number: 11911_60 N=18935897354626173534745801627323526764844167635587724246545604319900046630019556936284612994323149 ( 98 digits) SNFS difficulty: 121 digits. Divisors found: r1=18603945024252359647586172479299347296895947 (pp44) r2=1017843114992066265791411519193442648002770541494100167 (pp55) Version: GGNFS-0.77.0 Total time: 3.85 hours. Scaled time: 1.99 units (timescale=0.517). Factorization parameters were as follows: n: 18935897354626173534745801627323526764844167635587724246545604319900046630019556936284612994323149 m: 1000000000000000000000000000000 c4: 10 c2: 72 c0: -1 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 750001) Relations: rels:1953840, finalFF:155694 Initial matrix: 112777 x 155694 with sparse part having weight 12620463. Pruned matrix : 107652 x 108279 with weight 5697265. Total sieving time: 3.53 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.22 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.85 hours. --------- CPU info (if available) ----------

(10¹²⁵+54·10⁶²-1)/9 = 11111111111111111111111111111111111111111111111111111111111111711111111111111111111111111111111111111111111111111111111111111_<125> = 7 · 17 · 317 · C120
C120 = P40 · P80
P40 = 7973322074105264033384947437846009001513_<40>
P80 = 36941281712920258112424104486852540883846738400367841483096109228211987802564989_<80>

Number: 11711_62 N=294544736927368213321080272277154815659176394006603693001911611248074413782337330305413437719988100392628134324181828357 ( 120 digits) SNFS difficulty: 125 digits. Divisors found: r1=7973322074105264033384947437846009001513 (pp40) r2=36941281712920258112424104486852540883846738400367841483096109228211987802564989 (pp80) Version: GGNFS-0.77.0 Total time: 4.43 hours. Scaled time: 2.05 units (timescale=0.464). Factorization parameters were as follows: n: 294544736927368213321080272277154815659176394006603693001911611248074413782337330305413437719988100392628134324181828357 m: 10000000000000000000000000000000 c4: 10 c2: 54 c0: -1 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 800001) Relations: rels:1845599, finalFF:135937 Initial matrix: 113024 x 135937 with sparse part having weight 10344713. Pruned matrix : 110853 x 111482 with weight 6388512. Total sieving time: 4.07 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.25 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,125,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.43 hours. --------- CPU info (if available) ----------

(10¹²⁵+6·10⁶²-1)/3 = 33333333333333333333333333333333333333333333333333333333333333533333333333333333333333333333333333333333333333333333333333333_<125> = 743 · 6737 · C118
C118 = P50 · P69
P50 = 36758479527898023340004448251397139898197187184737_<50>
P69 = 181161473815681904121219350710639752665780284481427976281055477903699_<69>

Number: 33533_62 N=6659220326497577075980305489068789945749329766122188835111245312158610907949397650214197151411957815437444516208642163 ( 118 digits) SNFS difficulty: 125 digits. Divisors found: r1=36758479527898023340004448251397139898197187184737 (pp50) r2=181161473815681904121219350710639752665780284481427976281055477903699 (pp69) Version: GGNFS-0.77.0 Total time: 4.94 hours. Scaled time: 2.48 units (timescale=0.502). Factorization parameters were as follows: n: 6659220326497577075980305489068789945749329766122188835111245312158610907949397650214197151411957815437444516208642163 m: 10000000000000000000000000000000 c4: 10 c2: 6 c0: -1 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 850001) Relations: rels:1877389, finalFF:126846 Initial matrix: 112756 x 126846 with sparse part having weight 10771632. Pruned matrix : 111361 x 111988 with weight 8080776. Total sieving time: 4.53 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.30 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,125,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.94 hours. --------- CPU info (if available) ----------

(7·10¹²⁵-18·10⁶²-7)/9 = 77777777777777777777777777777777777777777777777777777777777777577777777777777777777777777777777777777777777777777777777777777_<125> = 3² · 47475031 · 120939911024162888803_<21> · C97
C97 = P38 · P59
P38 = 60970037018125996965377217842992612127_<38>
P59 = 24686621629077471969947980022232477103969504451669996673323_<59>

Number: 77577_62 N=1505144234577323370608265076869619977152542106177086227670600044322931113862861205128956067188021 ( 97 digits) SNFS difficulty: 125 digits. Divisors found: r1=60970037018125996965377217842992612127 (pp38) r2=24686621629077471969947980022232477103969504451669996673323 (pp59) Version: GGNFS-0.77.0 Total time: 5.94 hours. Scaled time: 3.05 units (timescale=0.513). Factorization parameters were as follows: n: 1505144234577323370608265076869619977152542106177086227670600044322931113862861205128956067188021 m: 10000000000000000000000000000000 c4: 70 c2: -18 c0: -7 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 950001) Relations: rels:2017584, finalFF:147669 Initial matrix: 112930 x 147669 with sparse part having weight 14603951. Pruned matrix : 110170 x 110798 with weight 8204709. Total sieving time: 5.51 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.30 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,125,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 5.94 hours. --------- CPU info (if available) ----------

(7·10¹²⁵+9·10⁶²-7)/9 = 77777777777777777777777777777777777777777777777777777777777777877777777777777777777777777777777777777777777777777777777777777_<125> = 3 · 99524603534812785324188777_<26> · C99
C99 = P47 · P53
P47 = 19672192045799176624374177119391737000240110877_<47>
P53 = 13241923182778468223372021017297185130734815430594271_<53>

Number: 77877_62 N=260497655907338299050539410778430931302480341020225880621971057677621936464392053126200123040985667 ( 99 digits) SNFS difficulty: 125 digits. Divisors found: r1=19672192045799176624374177119391737000240110877 (pp47) r2=13241923182778468223372021017297185130734815430594271 (pp53) Version: GGNFS-0.77.0 Total time: 5.84 hours. Scaled time: 2.94 units (timescale=0.504). Factorization parameters were as follows: n: 260497655907338299050539410778430931302480341020225880621971057677621936464392053126200123040985667 m: 10000000000000000000000000000000 c4: 70 c2: 9 c0: -7 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 950001) Relations: rels:2062439, finalFF:167522 Initial matrix: 112676 x 167522 with sparse part having weight 16536364. Pruned matrix : 108237 x 108864 with weight 7240777. Total sieving time: 5.46 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.26 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,125,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 5.84 hours. --------- CPU info (if available) ----------

Jun 2, 2005 (2nd)

By Yousuke Koide / GMP-ECM
(10⁵²⁷-1)/9 = (1)_527<527> = 2791 · 825283 · 2071723 · 6943319 · 5363222357_<10> · 453741012227_<12> · 57336415063790604359_<20> · C463
C463 = P38 · C426
P38 = 12608116535176707758425943211733416917_<38>
C426 = [190625660033367623649366513850342668718630676435603017730438925147731244725702111038256432946058271374588741522536113019723779437628690678571832318225680756653169739489393595038914321065173043105819480187509134710831868143295081706886253115187112460797498234027556715949116962709528956942516510922386827195216182552009620219645172828917942646747626396693510781549829166660527911776684936435549302982040368984708536912296472003_<426>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 2, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(10¹²³+54·10⁶¹-1)/9 = 111111111111111111111111111111111111111111111111111111111111171111111111111111111111111111111111111111111111111111111111111_<123> = 3 · 19 · 163 · 739 · 1933727 · C109
C109 = P50 · P60
P50 = 24177014076442824163935261435022122376098464369513_<50>
P60 = 346140779655288965633172120469218510283083951282762618834289_<60>

Number: 11711_61 N=8368650502156815251315435496144790676963884516443182209963302915957985851729118082729617851799027005410631257 ( 109 digits) SNFS difficulty: 124 digits. Divisors found: r1=24177014076442824163935261435022122376098464369513 (pp50) r2=346140779655288965633172120469218510283083951282762618834289 (pp60) Version: GGNFS-0.77.0 Total time: 4.36 hours. Scaled time: 2.29 units (timescale=0.525). Factorization parameters were as follows: n: 8368650502156815251315435496144790676963884516443182209963302915957985851729118082729617851799027005410631257 m: 10000000000000000000000000000000 c4: 1 c2: 54 c0: -10 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 800001) Relations: rels:1922294, finalFF:164446 Initial matrix: 113042 x 164446 with sparse part having weight 12521145. Pruned matrix : 108306 x 108935 with weight 5022358. Total sieving time: 4.07 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.20 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,124,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.36 hours. --------- CPU info (if available) ----------

(10¹²³+72·10⁶¹-1)/9 = 111111111111111111111111111111111111111111111111111111111111191111111111111111111111111111111111111111111111111111111111111_<123> = 830741 · C117
C117 = P57 · P60
P57 = 333943384135918323799284829426734387858561633507038519893_<57>
P60 = 400515199053720590198605795341928759454360997189738245325247_<60>

Number: 11911_61 N=133749400969870406192918263467327495706978602369584637222806134657024404851946769343406803216780092846159165264638571 ( 117 digits) SNFS difficulty: 124 digits. Divisors found: r1=333943384135918323799284829426734387858561633507038519893 (pp57) r2=400515199053720590198605795341928759454360997189738245325247 (pp60) Version: GGNFS-0.77.0 Total time: 4.75 hours. Scaled time: 2.46 units (timescale=0.517). Factorization parameters were as follows: n: 133749400969870406192918263467327495706978602369584637222806134657024404851946769343406803216780092846159165264638571 m: 10000000000000000000000000000000 c4: 1 c2: 72 c0: -10 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 850001) Relations: rels:2002893, finalFF:178465 Initial matrix: 112642 x 178465 with sparse part having weight 15245143. Pruned matrix : 106754 x 107381 with weight 5458667. Total sieving time: 4.45 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.21 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,124,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.75 hours. --------- CPU info (if available) ----------

(10¹²³+6·10⁶¹-1)/3 = 333333333333333333333333333333333333333333333333333333333333353333333333333333333333333333333333333333333333333333333333333_<123> = 17 · C122
C122 = P47 · P75
P47 = 27814144339367109918804963147451053819016220333_<47>
P75 = 704959422731645455575289184902418785159553295349154642026036197242998215353_<75>

Number: 33533_61 N=19607843137254901960784313725490196078431372549019607843137256078431372549019607843137254901960784313725490196078431372549 ( 122 digits) SNFS difficulty: 124 digits. Divisors found: r1=27814144339367109918804963147451053819016220333 (pp47) r2=704959422731645455575289184902418785159553295349154642026036197242998215353 (pp75) Version: GGNFS-0.77.0 Total time: 4.31 hours. Scaled time: 2.22 units (timescale=0.514). Factorization parameters were as follows: n: 19607843137254901960784313725490196078431372549019607843137256078431372549019607843137254901960784313725490196078431372549 m: 10000000000000000000000000000000 c4: 1 c2: 6 c0: -10 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 800001) Relations: rels:1864426, finalFF:139284 Initial matrix: 112982 x 139284 with sparse part having weight 10485798. Pruned matrix : 110583 x 111211 with weight 6085535. Total sieving time: 3.98 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.25 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,124,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.31 hours. --------- CPU info (if available) ----------

(7·10¹²³-45·10⁶¹-7)/9 = 777777777777777777777777777777777777777777777777777777777777727777777777777777777777777777777777777777777777777777777777777_<123> = 23 · 70924381691_<11> · C111
C111 = P49 · P62
P49 = 6449837247782303232093281784658518590839975860721_<49>
P62 = 73923646265105422719114933120555496355101491772474460906208709_<62>

Number: 77277_61 N=476795487172560099236739945180836688228943989965368243984533468565741111902447129669718872492083435995141219189 ( 111 digits) SNFS difficulty: 124 digits. Divisors found: r1=6449837247782303232093281784658518590839975860721 (pp49) r2=73923646265105422719114933120555496355101491772474460906208709 (pp62) Version: GGNFS-0.77.0 Total time: 5.32 hours. Scaled time: 2.70 units (timescale=0.508). Factorization parameters were as follows: n: 476795487172560099236739945180836688228943989965368243984533468565741111902447129669718872492083435995141219189 m: 10000000000000000000000000000000 c4: 7 c2: -45 c0: -70 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 900001) Relations: rels:1992194, finalFF:160633 Initial matrix: 112945 x 160633 with sparse part having weight 14658643. Pruned matrix : 109130 x 109758 with weight 6724701. Total sieving time: 4.96 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.26 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,124,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 5.32 hours. --------- CPU info (if available) ----------

Jun 1, 2005 (3rd)

By Anton Korobeynikov / GGNFS-0.77.1
(10¹²⁷+45·10⁶³-1)/9 = 1111111111111111111111111111111111111111111111111111111111111116111111111111111111111111111111111111111111111111111111111111111_<127> = 3 · 29 · 113 · 20039627 · 17943655390847_<14> · C102
C102 = P45 · P57
P45 = 388892054665769589332251337459778952118466577_<45>
P57 = 808221074329162557129786383917012036277024262407706022637_<57>

Number: gnfs8 N=314310754220043711687892510706249953140553848186409630996780015742951816371022475594518847348089903549 ( 102 digits) Divisors found: r1=388892054665769589332251337459778952118466577 (pp45) r2=808221074329162557129786383917012036277024262407706022637 (pp57) Version: GGNFS-0.77.1 Total time: 10.57 hours. Scaled time: 10.05 units (timescale=0.951). Factorization parameters were as follows: name: gnfs8 n: 314310754220043711687892510706249953140553848186409630996780015742951816371022475594518847348089903549 skew: 8020.53 # norm 1.24e+014 c5: 81900 c4: 958525056 c3: -8399637298891 c2: -51851268458066371 c1: -7008102930395279189 c0: 653324131452677932541295 # alpha -6.22 Y1: 14806327663 Y0: -20740266957471591364 # Murphy_E 2.85e-009 # M 37358659076484039915362325711913352536141497804833547942517755482835183282465168705003579414882783923 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1150000, 1750001) Relations: rels:4327228, finalFF:438560 Initial matrix: 339049 x 438560 with sparse part having weight 30684901. Pruned matrix : 292635 x 294394 with weight 13463839. Polynomial selection time: 0.33 hours. Total sieving time: 8.66 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.21 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 10.57 hours. --------- CPU info (if available) ----------

Jun 1, 2005 (2nd)

By Makoto Kamada / GMP-ECM 6.0.1
(4·10¹⁷⁵+23)/9 = (4)₁₇₄7_<175> = 7⁴ · 151 · 4077068417_<10> · 912028673482967_<15> · C145
C145 = P32 · C114
P32 = 18287204296526384115739261382729_<32>
C114 = [180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087_<114>]
(10¹³⁹+6·10⁶⁹-1)/3 = 3333333333333333333333333333333333333333333333333333333333333333333335333333333333333333333333333333333333333333333333333333333333333333333_<139> = 4423 · 7690519 · C128
C128 = P30 · P99
P30 = 257984303314597788657955894013_<30>
P99 = 379850649833740727794024738173681159907765233717802570010963219776843219340065788338846223366687193_<99>

Jun 1, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(7·10¹¹⁹-9·10⁵⁹-7)/9 = 77777777777777777777777777777777777777777777777777777777777677777777777777777777777777777777777777777777777777777777777_<119> = 59 · 101312879 · C110
C110 = P52 · P59
P52 = 1055735817849591341311284793442382288948131189800529_<52>
P59 = 12324905726071694420147494916645611671169597636672802224733_<59>

Number: 77677_59 N=13011844426633411696577142064020591468054991892446231480897212799833099168305360834237775532889986189700283757 ( 110 digits) SNFS difficulty: 120 digits. Divisors found: r1=1055735817849591341311284793442382288948131189800529 (pp52) r2=12324905726071694420147494916645611671169597636672802224733 (pp59) Version: GGNFS-0.77.0 Total time: 3.44 hours. Scaled time: 1.81 units (timescale=0.526). Factorization parameters were as follows: n: 13011844426633411696577142064020591468054991892446231480897212799833099168305360834237775532889986189700283757 m: 1000000000000000000000000000000 c4: 7 c2: -9 c0: -70 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 700001) Relations: rels:2033915, finalFF:206716 Initial matrix: 112674 x 206716 with sparse part having weight 16486606. Pruned matrix : 99880 x 100507 with weight 4201408. Total sieving time: 3.20 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.15 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,120,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.44 hours. --------- CPU info (if available) ----------

10¹¹⁹-2·10⁵⁹-1 = 99999999999999999999999999999999999999999999999999999999999799999999999999999999999999999999999999999999999999999999999_<119> = 11 · 317 · 4463 · C112
C112 = P43 · P70
P43 = 3167237723290723022627763701000062201290487_<43>
P70 = 2028805924177070278738189526016446215925057127787218042322616836553417_<70>

Number: 99799_59 N=6425710656289315309043590157636176391155112092988258106146429994035012797766628598614835256666337456090709444079 ( 112 digits) SNFS difficulty: 120 digits. Divisors found: r1=3167237723290723022627763701000062201290487 (pp43) r2=2028805924177070278738189526016446215925057127787218042322616836553417 (pp70) Version: GGNFS-0.77.0 Total time: 3.34 hours. Scaled time: 1.79 units (timescale=0.536). Factorization parameters were as follows: n: 6425710656289315309043590157636176391155112092988258106146429994035012797766628598614835256666337456090709444079 m: 1000000000000000000000000000000 c4: 1 c2: -2 c0: -10 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 700001) Relations: rels:1977300, finalFF:185338 Initial matrix: 112808 x 185338 with sparse part having weight 14329446. Pruned matrix : 102276 x 102904 with weight 4355231. Total sieving time: 3.10 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.16 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,120,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.34 hours. --------- CPU info (if available) ----------

(10¹²¹+12·10⁶⁰-1)/3 = 3333333333333333333333333333333333333333333333333333333333337333333333333333333333333333333333333333333333333333333333333_<121> = 7 · 23 · 1051 · C116
C116 = P32 · P85
P32 = 11577286871594539754300974611271_<32>
P85 = 1701544683868553106986624465217486015780816568224111390083016841578865269040518765593_<85>

Number: 33733_60 N=19699270929982881333561844876121134756802650733896338496512267720971646839350475638896604436669798850744533944798703 ( 116 digits) SNFS difficulty: 121 digits. Divisors found: r1=11577286871594539754300974611271 (pp32) r2=1701544683868553106986624465217486015780816568224111390083016841578865269040518765593 (pp85) Version: GGNFS-0.77.0 Total time: 2.84 hours. Scaled time: 1.50 units (timescale=0.529). Factorization parameters were as follows: n: 19699270929982881333561844876121134756802650733896338496512267720971646839350475638896604436669798850744533944798703 m: 1000000000000000000000000000000 c4: 10 c2: 12 c0: -1 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 650001) Relations: rels:1815599, finalFF:140222 Initial matrix: 112879 x 140222 with sparse part having weight 9965266. Pruned matrix : 104985 x 105613 with weight 5387966. Total sieving time: 2.56 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.19 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.84 hours. --------- CPU info (if available) ----------

10¹²¹-5·10⁶⁰-1 = 9999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999_<121> = 165149106706211_<15> · C107
C107 = P50 · P58
P50 = 27611806515679263468269678707072310135743844147387_<50>
P58 = 2192951110112010923330726818171905685664179773222579832207_<58>

Number: 99499_60 N=60551341750756897169375054885967551734285315006056608046414443048414744433045704281283606426609557437493109 ( 107 digits) SNFS difficulty: 121 digits. Divisors found: r1=27611806515679263468269678707072310135743844147387 (pp50) r2=2192951110112010923330726818171905685664179773222579832207 (pp58) Version: GGNFS-0.77.0 Total time: 3.35 hours. Scaled time: 1.80 units (timescale=0.537). Factorization parameters were as follows: n: 60551341750756897169375054885967551734285315006056608046414443048414744433045704281283606426609557437493109 m: 1000000000000000000000000000000 c4: 10 c2: -5 c0: -1 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 700001) Relations: rels:1995927, finalFF:187028 Initial matrix: 113116 x 187028 with sparse part having weight 15033671. Pruned matrix : 102851 x 103480 with weight 4651587. Total sieving time: 3.10 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.17 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121,4,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.35 hours. --------- CPU info (if available) ----------