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STUDIO KAMADA

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News and updates, April 2007

Apr 30, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000
(10¹⁷⁶+17)/9 = (1)₁₇₅3_<176> = 13 · 1879391 · 6718199 · C161
C161 = P35 · C127
P35 = 43731936268508244866927446133249317_<35>
C127 = [1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017_<127>]

Apr 29, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000
(10¹⁹⁸+17)/9 = (1)₁₉₇3_<198> = 10903 · 14765887 · 30620063 · C179
C179 = P37 · P143
P37 = 1106470306688059445573370198780657763_<37>
P143 = 20370706632593519622375724577942747394309044829544818549592211014459360143604890305766200820243688122193921133924400853893810356993408166701557_<143>

Apr 29, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁶²+1)/3 = 1(6)₁₆₁7_<163> = 67 · C161
C161 = P77 · P85
P77 = 15021343982458863265099067005237957428313579616162543134808299151295298507741_<77>
P85 = 1656018390870730922037745080017419987395416242647949264972839350025244821735227203661_<85>

Number: n N=24875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039801 ( 161 digits) SNFS difficulty: 162 digits. Divisors found: r1=15021343982458863265099067005237957428313579616162543134808299151295298507741 (pp77) r2=1656018390870730922037745080017419987395416242647949264972839350025244821735227203661 (pp85) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.32 hours. Scaled time: 58.51 units (timescale=1.451). Factorization parameters were as follows: name: KA_1_6_161_7 n: 24875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039801 skew: 0.29 deg: 5 c5: 500 c0: 1 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2100001) Primes: RFBsize:216816, AFBsize:216391, largePrimes:7234005 encountered Relations: rels:6721359, finalFF:495113 Max relations in full relation-set: 28 Initial matrix: 433273 x 495113 with sparse part having weight 39011344. Pruned matrix : 387351 x 389581 with weight 27248773. Total sieving time: 35.60 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.43 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 40.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

P77 is the fourth largest factor found by GGNFS so far in our tables. Congratulations!
See Records.
(83·10¹⁶⁰+61)/9 = 9(2)₁₅₉9_<161> = 3 · C161
C161 = P60 · P101
P60 =763644251892931073537547192111224194051499190901748667513491_<60>
P101 = 40255316090627542913753162624598825771292696705345565195696208829537695183338310830115705652897654973_<101>

Number: n N=30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 ( 161 digits) SNFS difficulty: 161 digits. Divisors found: r1=763644251892931073537547192111224194051499190901748667513491 (pp60) r2=40255316090627542913753162624598825771292696705345565195696208829537695183338310830115705652897654973 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 61.80 hours. Scaled time: 73.97 units (timescale=1.197). Factorization parameters were as follows: name: KA_9_2_159_9 n: 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 type: snfs skew: 0.94 deg: 5 c5: 83 c0: 61 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2500001) Primes: RFBsize:216816, AFBsize:216307, largePrimes:7209488 encountered Relations: rels:6639658, finalFF:486906 Max relations in full relation-set: 28 Initial matrix: 433188 x 486906 with sparse part having weight 36566778. Pruned matrix : 396137 x 398366 with weight 26704077. Total sieving time: 56.15 hours. Total relation processing time: 0.27 hours. Matrix solve time: 5.25 hours. Total square root time: 0.13 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 61.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 28, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(82·10¹⁵⁹-1)/9 = 9(1)_159<160> = 3 · C160
C160 = P48 · P113
P48 = 241647557727089005892292451432908599283904128733_<48>
P113 = 12568043582161895072963384363446372944023458284330325387157152352247464883030826446963412997874721323844798980689_<113>

Number: n N=3037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037 ( 160 digits) SNFS difficulty: 161 digits. Divisors found: r1=241647557727089005892292451432908599283904128733 (pp48) r2=12568043582161895072963384363446372944023458284330325387157152352247464883030826446963412997874721323844798980689 (pp113) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 45.19 hours. Scaled time: 61.95 units (timescale=1.371). Factorization parameters were as follows: name: KA_9_1_159 n: 3037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037 skew: 0.66 deg: 5 c5: 41 c0: -5 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1900001) Primes: RFBsize:216816, AFBsize:216857, largePrimes:7255543 encountered Relations: rels:6763085, finalFF:512657 Max relations in full relation-set: 28 Initial matrix: 433738 x 512657 with sparse part having weight 40151255. Pruned matrix : 373681 x 375913 with weight 26539749. Total sieving time: 40.91 hours. Total relation processing time: 0.25 hours. Matrix solve time: 3.52 hours. Total square root time: 0.51 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 45.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(5·10¹⁶¹+31)/9 = (5)₁₆₀9_<161> = 7 · C160
C160 = P49 · P51 · P62
P49 = 2438969913365590123358917315136313969549616824191_<49>
P51 = 126382113975161545904668128138667915671155888382263_<51>
P62 = 25747638113606124053747971056356175569815887788007147104126489_<62>

Number: n N=7936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937 ( 160 digits) SNFS difficulty: 161 digits. Divisors found: r1=2438969913365590123358917315136313969549616824191 (pp49) r2=126382113975161545904668128138667915671155888382263 (pp51) r3=25747638113606124053747971056356175569815887788007147104126489 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 50.81 hours. Scaled time: 67.32 units (timescale=1.325). Factorization parameters were as follows: name: KA_5_160_9 n: 7936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937 skew: 0.91 deg: 5 c5: 50 c0: 31 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2200001) Primes: RFBsize:216816, AFBsize:217337, largePrimes:7429297 encountered Relations: rels:6959464, finalFF:557409 Max relations in full relation-set: 48 Initial matrix: 434218 x 557409 with sparse part having weight 52928452. Pruned matrix : 357779 x 360014 with weight 31099006. Total sieving time: 45.45 hours. Total relation processing time: 0.25 hours. Matrix solve time: 4.87 hours. Total square root time: 0.24 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 50.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 28, 2007

By Yousuke Koide / GMP-ECM B1=1e6 / Apr 25, 2007
10¹⁸¹⁰+1 = 1(0)₁₈₀₉1_<1811> = 101 · 3541 · 27961 · 928417781 · 3655211741_<10> · 469968172441_<12> · 2136569912461_<13> · 196636530190361_<15> · 263346017179961_<15> · 15470952779187481_<17> · 3294170239985256241_<19> · 3467369151629862044701_<22> · 3973728652754811772515860861_<28> · 314547891171506427278717744569_<30> · 22780106292572351730658730234738216404394547689_<47> · 2763057708101686443032907255670870301200401399657924257107762182149956480304265507465823191458543338192444247826866701172774820848970862394309509034525824920430145923354279701799097867258088089212682054699054590801_<214> · C651 · C706
C706 = P38 · C668
P38 = 81685556537224955443340015680020142181_<38>
By Yousuke Koide / GMP-ECM B1=125e4 / Apr 28, 2007
(10⁷⁸⁷-1)/9 = (1)_787<787> = 26759 · 213141637 · C774
C774 = P34 · C741
P34 = 1074022836653095912870566750079013_<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 27, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=548000, B1=580000
(32·10¹⁶¹-23)/9 = 3(5)₁₆₀3_<162> = 11 · C161
C161 = P35 · P36 · P91
P35 = 27259050424085339529239969264230591_<35>
P36 = 803134225042376363531999194958705621_<36>
P91 = 1476440423481398408509200960925473650542806915465777143424498012793825455523287350714672393_<91>

Apr 26, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁹-7)/3 = 1(3)₁₅₈1_<160> = 11 · 23 · C157
C157 = P53 · P105
P53 = 17459658467387443869331205970366143563395038136006397_<53>
P105 = 301843947088533742600289415675999685198956945601568904220026735567745228859461977377699316648532130087291_<105>

Number: n N=5270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527 ( 157 digits) SNFS difficulty: 160 digits. Divisors found: r1=17459658467387443869331205970366143563395038136006397 (pp53) r2=301843947088533742600289415675999685198956945601568904220026735567745228859461977377699316648532130087291 (pp105) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 27.80 hours. Scaled time: 37.95 units (timescale=1.365). Factorization parameters were as follows: name: KA_1_3_158_1 n: 5270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527 skew: 1.77 deg: 5 c5: 2 c0: -35 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216006, largePrimes:6763878 encountered Relations: rels:6238378, finalFF:487616 Max relations in full relation-set: 28 Initial matrix: 432887 x 487616 with sparse part having weight 29932096. Pruned matrix : 383769 x 385997 with weight 19502837. Total sieving time: 24.57 hours. Total relation processing time: 0.24 hours. Matrix solve time: 2.79 hours. Total square root time: 0.20 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 27.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

2·10¹⁵⁸-9 = 1(9)₁₅₇1_<159> = 449 · 647 · 263423 · C148
C148 = P59 · P90
P59 = 24629981367007296663635744349139127212651564923379917379247_<59>
P90 = 106111291216604957235287331858373630426835509120007905601583219050565604016518888425492737_<90>

Number: n N=2613519125494065116104920898710776208411387878266129214050977218917923341224771005061211782302690175095868199383407515341058443407151053865673029039 ( 148 digits) SNFS difficulty: 158 digits. Divisors found: r1=24629981367007296663635744349139127212651564923379917379247 (pp59) r2=106111291216604957235287331858373630426835509120007905601583219050565604016518888425492737 (pp90) Version: GGNFS-0.77.1-20051202-athlon Total time: 37.18 hours. Scaled time: 44.43 units (timescale=1.195). Factorization parameters were as follows: name: KA_1_9_157_1 n: 2613519125494065116104920898710776208411387878266129214050977218917923341224771005061211782302690175095868199383407515341058443407151053865673029039 type: snfs skew: 0.68 deg: 5 c5: 125 c0: -18 m: 20000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:216826, largePrimes:6772566 encountered Relations: rels:6340882, finalFF:591658 Max relations in full relation-set: 28 Initial matrix: 433708 x 591658 with sparse part having weight 33045348. Pruned matrix : 297330 x 299562 with weight 16786027. Total sieving time: 34.67 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.20 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 37.18 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(65·10¹⁵⁸+43)/9 = 7(2)₁₅₇7_<159> = 19 · 7448303743_<10> · C148
C148 = P70 · P79
P70 = 2283906434721397222715225004575163162522053541582590209420748519155831_<70>
P79 = 2234506175283351071706709697979013414681324521591035009309462144344402039107001_<79>

Number: n N=5103403032154343834741178855604673819491372467573218373515476529946980780374398851423525859559148205166416041259945688339089065263392267437602072831 ( 148 digits) SNFS difficulty: 160 digits. Divisors found: r1=2283906434721397222715225004575163162522053541582590209420748519155831 (pp70) r2=2234506175283351071706709697979013414681324521591035009309462144344402039107001 (pp79) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.27 hours. Scaled time: 63.86 units (timescale=1.323). Factorization parameters were as follows: name: KA_7_2_157_7 n: 5103403032154343834741178855604673819491372467573218373515476529946980780374398851423525859559148205166416041259945688339089065263392267437602072831 skew: 1.16 deg: 5 c5: 104 c0: 215 m: 50000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:216816, AFBsize:216546, largePrimes:7326828 encountered Relations: rels:6829370, finalFF:530036 Max relations in full relation-set: 48 Initial matrix: 433428 x 530036 with sparse part having weight 48883949. Pruned matrix : 366007 x 368238 with weight 29896532. Total sieving time: 42.64 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.80 hours. Total square root time: 0.60 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 48.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(4·10¹⁵⁹-13)/9 = (4)₁₅₈3_<159> = 19 · C158
C157 = P32 · P60 · P67
P32 = 84189747192092171468535381286471_<32>
P60 = 154525079685364105720550993011600245901181046815079559422881_<60>
P67 = 1798066291303254277894237143922564989013145315594815253125477086847_<67>

Number: n N=23391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497 ( 158 digits) SNFS difficulty: 160 digits. Divisors found: r1=84189747192092171468535381286471 (pp32) r2=154525079685364105720550993011600245901181046815079559422881 (pp60) r3=1798066291303254277894237143922564989013145315594815253125477086847 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.54 hours. Scaled time: 57.33 units (timescale=1.450). Factorization parameters were as follows: name: KA_4_158_3 n: 23391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497 skew: 2.00 deg: 5 c5: 2 c0: -65 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1900001) Primes: RFBsize:216816, AFBsize:216126, largePrimes:7250354 encountered Relations: rels:6745505, finalFF:499663 Max relations in full relation-set: 28 Initial matrix: 433007 x 499663 with sparse part having weight 38893311. Pruned matrix : 382407 x 384636 with weight 26621486. Total sieving time: 34.75 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.30 hours. Total square root time: 0.29 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 39.54 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 26, 2007

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000
9·10¹⁸⁷+1 = 9(0)₁₈₆1_<188> = 7 · 13 · 4373 · 5717 · 20183 · C175
C175 = P32 · C143
P32 = 24068660737760877432355395211891_<32>
C143 = [81435881553600072016173523292608504397039692207307496066394773089520233394402320905105063604429647318463867320494190178646753385161893694575807_<143>]
9·10¹⁷⁶+1 = 9(0)₁₇₅1_<177> = 382561419661867013_<18> · C160
C160 = P34 · C126
P34 = 4153302760261926665697975045884449_<34>
C126 = [566431958152526346806249739676161934366904899317226070390042476342664318676795495580542611504898377157441268210176302406249773_<126>]

Apr 25, 2007 (3rd)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000
9·10¹⁶⁴+1 = 9(0)₁₆₃1_<165> = 206021 · 987313 · 288154417 · C146
C146 = P33 · P113
P33 = 941596665917777874062834896326197_<33>
P113 = 16307446785923947920819586784374506111817003364273287474816055749579556455124440591984263685499136336546651516313_<113>

Apr 25, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000
(10¹⁹¹+53)/9 = (1)₁₉₀7_<191> = 83 · 257 · 2309 · 4481 · 30274753811_<11> · C169
C169 = P41 · P129
P41 = 14781772991827325758273699724307624723203_<41>
P129 = 112496820824306141289466401848140159736387544454873436102425778272976103436914816351733511282110806424845862379940475925100721451_<129>

Apr 25, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(14·10¹⁵⁸-41)/9 = 1(5)₁₅₇1_<159> = 29 · 31 · 32117 · C151
C151 = P74 · P78
P74 = 16890701960639836030505223027599141408171380796039886568589214265562803591_<74>
P78 = 318965097991281408955651198675474281172186567241455132017352484669834254010167_<78>

Number: n N=5387544406017014319327230238368785164959317286062833999131843397922409716848868223346056288825362813499140553902753137939643009070235018963983138109697 ( 151 digits) SNFS difficulty: 159 digits. Divisors found: r1=16890701960639836030505223027599141408171380796039886568589214265562803591 (pp74) r2=318965097991281408955651198675474281172186567241455132017352484669834254010167 (pp78) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 33.67 hours. Scaled time: 43.06 units (timescale=1.279). Factorization parameters were as follows: name: KA_1_5_157_1 n: 5387544406017014319327230238368785164959317286062833999131843397922409716848868223346056288825362813499140553902753137939643009070235018963983138109697 skew: 0.62 deg: 5 c5: 875 c0: -82 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:217337, largePrimes:7010678 encountered Relations: rels:6493609, finalFF:497084 Max relations in full relation-set: 28 Initial matrix: 434219 x 497084 with sparse part having weight 34384792. Pruned matrix : 382432 x 384667 with weight 22554464. Total sieving time: 30.59 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.75 hours. Total square root time: 0.11 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 33.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(13·10¹⁵⁸-31)/9 = 1(4)₁₅₇1_<159> = 3² · 59 · 1151 · 1259 · C150
C150 = P40 · P110
P40 = 2666207182373154418160383393318256974037_<40>
P110 = 70406276040739502591454509881526959077496256123980929796389336194469708080034764900330162435965741985863807867_<110>

Number: n N=187717718863966599371265116913856542848046308152222523692546770394181583257740021639356423657330507580390137290199780576440743769826051452345775349079 ( 150 digits) SNFS difficulty: 159 digits. Divisors found: r1=2666207182373154418160383393318256974037 (pp40) r2=70406276040739502591454509881526959077496256123980929796389336194469708080034764900330162435965741985863807867 (pp110) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.69 hours. Scaled time: 51.68 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_4_157_1 n: 187717718863966599371265116913856542848046308152222523692546770394181583257740021639356423657330507580390137290199780576440743769826051452345775349079 skew: 0.30 deg: 5 c5: 13000 c0: -31 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:216816, AFBsize:217162, largePrimes:7086581 encountered Relations: rels:6568699, finalFF:493501 Max relations in full relation-set: 28 Initial matrix: 434045 x 493501 with sparse part having weight 35899314. Pruned matrix : 385935 x 388169 with weight 24270637. Total sieving time: 31.12 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.85 hours. Total square root time: 0.50 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 35.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 24, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(67·10¹⁵⁸+23)/9 = 7(4)₁₅₇7_<159> = 3 · 31 · 1709 · C154
C154 = P44 · P111
P44 = 29260919942103733509905823159085703681886443_<44>
P111 = 160073450317003468362082050116843117920380447672897296042460127280985936066587164006989343231612150440123554917_<111>

Number: n N=4683896414582157989923330907494443990036583328264937959345177299461072276716211105308672269166049720609074315259784974200119823857531251026786993868290231 ( 154 digits) SNFS difficulty: 159 digits. Divisors found: r1=29260919942103733509905823159085703681886443 (pp44) r2=160073450317003468362082050116843117920380447672897296042460127280985936066587164006989343231612150440123554917 (pp111) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.41 hours. Scaled time: 51.55 units (timescale=1.308). Factorization parameters were as follows: name: KA_7_4_157_7 n: 4683896414582157989923330907494443990036583328264937959345177299461072276716211105308672269166049720609074315259784974200119823857531251026786993868290231 skew: 0.20 deg: 5 c5: 67000 c0: 23 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:216816, AFBsize:217321, largePrimes:7168927 encountered Relations: rels:6688652, finalFF:543810 Max relations in full relation-set: 48 Initial matrix: 434204 x 543810 with sparse part having weight 44745238. Pruned matrix : 347629 x 349864 with weight 25223265. Total sieving time: 35.47 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.64 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 39.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(5·10¹⁵⁸+13)/9 = (5)₁₅₇7_<158> = 3³ · C157
C157 = P33 · P124
P33 = 382853825496553598188403176353457_<33>
P124 = 5374409322031972772894913517826689979791154924734271046070635240945189138433355533839639709026504877244886570211096873586863_<124>

Number: n N=2057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835391 ( 157 digits) SNFS difficulty: 159 digits. Divisors found: r1=382853825496553598188403176353457 (pp33) r2=5374409322031972772894913517826689979791154924734271046070635240945189138433355533839639709026504877244886570211096873586863 (pp124) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.40 hours. Scaled time: 27.15 units (timescale=0.598). Factorization parameters were as follows: name: KA_5_157_7 n: 2057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835391 type: snfs skew: 1.52 deg: 5 c5: 8 c0: 65 m: 50000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:216816, AFBsize:217216, largePrimes:6949869 encountered Relations: rels:6482428, finalFF:569218 Max relations in full relation-set: 28 Initial matrix: 434097 x 569218 with sparse part having weight 35384681. Pruned matrix : 323170 x 325404 with weight 19605330. Total sieving time: 40.67 hours. Total relation processing time: 0.24 hours. Matrix solve time: 4.31 hours. Total square root time: 0.17 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 45.40 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+ (Timesharing)

Apr 23, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000
9·10¹⁹⁴+1 = 9(0)₁₉₃1_<195> = 17 · 1249 · 8089 · 1037297 · 106869415441_<12> · C170
C170 = P34 · P136
P34 = 6800424794926771388308831050471833_<34>
P136 = 6950942827174514887338020534901240077527602856760093566826256645756923667399042440819259600295410278353642353978340831657491455631029153_<136>

Apr 23, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=124000, GGNFS-0.77.1-20060513-athlon-xp gnfs, GGNFS-0.77.1-20051202-athlon
(89·10¹⁵⁷+1)/9 = 9(8)₁₅₆9_<158> = 3 · 11 · 83 · 507109 · 7608147321531382277_<19> · C130
C130 = P30 · P45 · P56
P30 = 998766999662301920263579973857_<30>
P45 = 671276082185180309721450498078371896813263139_<45>
P56 = 13957571951968016563167181516143946350859587741613040809_<56>

Number: n N=9369384216734849844858838821136383764594390595025958560650767203742805702183608663516846355662439451 ( 100 digits) SNFS difficulty: 158 digits. Divisors found: r1=671276082185180309721450498078371896813263139 (pp45) r2=13957571951968016563167181516143946350859587741613040809 (pp56) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 30.98 hours. Scaled time: 42.35 units (timescale=1.367). Factorization parameters were as follows: name: KA_9_8_156_9 n: 9369384216734849844858838821136383764594390595025958560650767203742805702183608663516846355662439451 # n: 9357831762831592716696047258075955006494138738306098602738469766935052019174596543063795350498288700538403141385637434411425432507 skew: 0.16 deg: 5 c5: 8900 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:217461, largePrimes:6928854 encountered Relations: rels:6418255, finalFF:501673 Max relations in full relation-set: 28 Initial matrix: 434344 x 501673 with sparse part having weight 33339151. Pruned matrix : 377922 x 380157 with weight 21090312. Total sieving time: 28.11 hours. Total relation processing time: 0.24 hours. Matrix solve time: 2.53 hours. Total square root time: 0.11 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 30.98 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(4·10¹⁵⁸-7)/3 = 1(3)₁₅₇1_<159> = 19 · C157
C157 = P57 · P101
P57 = 115570041668777500610211129739853968547382455176953878951_<57>
P101 = 60721132901910066040884017345234420133773553977363086094391872306702156725540345706908544495936768599_<101>

Number: n N=7017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649 ( 157 digits) SNFS difficulty: 158 digits. Divisors found: r1=115570041668777500610211129739853968547382455176953878951 (pp57) r2=60721132901910066040884017345234420133773553977363086094391872306702156725540345706908544495936768599 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.26 hours. Scaled time: 37.76 units (timescale=1.438). Factorization parameters were as follows: name: KA_1_3_157_1 n: 7017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649 skew: 0.56 deg: 5 c5: 125 c0: -7 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216506, largePrimes:6919954 encountered Relations: rels:6439560, finalFF:527050 Max relations in full relation-set: 28 Initial matrix: 433387 x 527050 with sparse part having weight 34175911. Pruned matrix : 352937 x 355167 with weight 19432489. Total sieving time: 23.13 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.78 hours. Total square root time: 0.17 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 26.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 22, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(13·10¹⁵⁶-1)/3 = 4(3)_156<157> = 482233522412249138299599463_<27> · C130
C130 = P51 · P80
P51 = 137685447586916374009095336332502139351312592931137_<51>
P80 = 65264446602257434699232134121438332071155454252336113787950688082621777887383843_<80>

Number: n N=8985964541944218457144242823891451622905412479065263958964874992630944518378669494178261920751344671254683705993473379975985419491 ( 130 digits) SNFS difficulty: 157 digits. Divisors found: r1=137685447586916374009095336332502139351312592931137 (pp51) r2=65264446602257434699232134121438332071155454252336113787950688082621777887383843 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.28 hours. Scaled time: 42.09 units (timescale=1.193). Factorization parameters were as follows: name: KA_4_3_156 n: 8985964541944218457144242823891451622905412479065263958964874992630944518378669494178261920751344671254683705993473379975985419491 type: snfs skew: 0.38 deg: 5 c5: 130 c0: -1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1400000) Primes: RFBsize:216816, AFBsize:216816, largePrimes:6426802 encountered Relations: rels:5897314, finalFF:498059 Max relations in full relation-set: 28 Initial matrix: 433699 x 498059 with sparse part having weight 28485229. Pruned matrix : 374897 x 377129 with weight 17607571. Total sieving time: 31.93 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.95 hours. Total square root time: 0.18 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 35.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(83·10¹⁵⁶+61)/9 = 9(2)₁₅₅9_<157> = 115603 · 31695397 · 11905360919303_<14> · C132
C132 = P45 · P88
P45 = 185694616568789821030958057358645587169415001_<45>
P88 = 1138487858025295935614061399440799079483198341134630811712967349874304476402618347315973_<88>

Number: n N=211411066264230152062340716870399973612067889013296080886298760548537066854582641830091382226851007304354037398622074774304913110973 ( 132 digits) SNFS difficulty: 157 digits. Divisors found: r1=185694616568789821030958057358645587169415001 (pp45) r2=1138487858025295935614061399440799079483198341134630811712967349874304476402618347315973 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 46.26 hours. Scaled time: 60.70 units (timescale=1.312). Factorization parameters were as follows: name: KA_9_2_155_9 n: 211411066264230152062340716870399973612067889013296080886298760548537066854582641830091382226851007304354037398622074774304913110973 skew: 0.59 deg: 5 c5: 830 c0: 61 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 18400001) Primes: RFBsize:216816, AFBsize:216337, largePrimes:7238483 encountered Relations: rels:6703027, finalFF:495978 Max relations in full relation-set: 48 Initial matrix: 433220 x 495978 with sparse part having weight 46386571. Pruned matrix : 387853 x 390083 with weight 30950811. Total sieving time: 40.61 hours. Total relation processing time: 0.25 hours. Matrix solve time: 5.13 hours. Total square root time: 0.28 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 46.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 22, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
6·10¹⁷¹+1 = 6(0)₁₇₀1_<172> = C172
C172 = P48 · P125
P48 = 154699561095803788960811837883435548718183965521_<48>
P125 = 38784854704818871237674570715604655076738950339421849949486353744053423298050903282396196418361477719330298221232535393256881_<125>

Number: 60001_171 N=6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ( 172 digits) SNFS difficulty: 171 digits. Divisors found: r1=154699561095803788960811837883435548718183965521 (pp48) r2=38784854704818871237674570715604655076738950339421849949486353744053423298050903282396196418361477719330298221232535393256881 (pp125) Version: GGNFS-0.77.1-20050930-k8 Total time: 121.74 hours. Scaled time: 109.20 units (timescale=0.897). Factorization parameters were as follows: n: 6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 m: 10000000000000000000000000000000000 c5: 60 c0: 1 skew: 1 type: snfs Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [4200000, 8300001) Primes: RFBsize:564877, AFBsize:563981, largePrimes:6631468 encountered Relations: rels:7286289, finalFF:1293157 Max relations in full relation-set: 28 Initial matrix: 1128925 x 1293157 with sparse part having weight 57494928. Pruned matrix : 980575 x 986283 with weight 39531468. Total sieving time: 115.09 hours. Total relation processing time: 0.17 hours. Matrix solve time: 6.39 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,8400000,8400000,27,27,49,49,2.6,2.6,100000 total time: 121.74 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.60 BogoMIPS (lpj=2335802) Calibrating delay using timer specific routine.. 4668.49 BogoMIPS (lpj=2334246) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 22, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁵-23)/9 = (5)₁₅₄3_<155> = 455809 · 22178359105380078019_<20> · C130
C130 = P41(7816...) · P41(9862...) · P48
P41(7816...) = 78168599768506389915769096471731999506381_<41>
P41(9862...) = 98627970534811576733762760709847556429329_<41>
P48 = 712824730143064724192573094052187772119187236807_<48>

Number: n N=5495600920608415791807485198227477664347272781973051325964290441482871529967054684754824258422291187953818426925644487404889381643 ( 130 digits) SNFS difficulty: 155 digits. Divisors found: r1=78168599768506389915769096471731999506381 (pp41) r2=98627970534811576733762760709847556429329 (pp41) r3=712824730143064724192573094052187772119187236807 (pp48) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 25.32 hours. Scaled time: 34.53 units (timescale=1.364). Factorization parameters were as follows: name: KA_5_154_3 n: 5495600920608415791807485198227477664347272781973051325964290441482871529967054684754824258422291187953818426925644487404889381643 skew: 1.36 deg: 5 c5: 5 c0: -23 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:217341, largePrimes:6728171 encountered Relations: rels:6204172, finalFF:487768 Max relations in full relation-set: 28 Initial matrix: 434222 x 487768 with sparse part having weight 30334453. Pruned matrix : 385580 x 387815 with weight 19867980. Total sieving time: 22.41 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.52 hours. Total square root time: 0.21 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(55·10¹⁵⁷-1)/9 = 6(1)_157<158> = 12659 · 5115353 · 2427133077049363_<16> · C132
C132 = P61 · P72
P61 = 1756885727384775588518191961618990892705830617844120872919597_<61>
P72 = 221313582188953735910104077220440356480321006702394425598594316859809763_<72>

Number: n N=388822673824170299517613128480124207165358916317761241208979819858125521756603961615264259628492731976257986840051227899003814625511 ( 132 digits) SNFS difficulty: 160 digits. Divisors found: r1=1756885727384775588518191961618990892705830617844120872919597 (pp61) r2=221313582188953735910104077220440356480321006702394425598594316859809763 (pp72) Version: GGNFS-0.77.1-20051202-athlon Total time: 37.76 hours. Scaled time: 54.64 units (timescale=1.447). Factorization parameters were as follows: name: KA_6_1_157 n: 388822673824170299517613128480124207165358916317761241208979819858125521756603961615264259628492731976257986840051227899003814625511 skew: 0.89 deg: 5 c5: 44 c0: -25 m: 50000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:216816, AFBsize:217237, largePrimes:7155233 encountered Relations: rels:6639789, finalFF:492384 Max relations in full relation-set: 28 Initial matrix: 434120 x 492384 with sparse part having weight 37041926. Pruned matrix : 389521 x 391755 with weight 25693721. Total sieving time: 33.10 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.39 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 37.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 21, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
4·10¹⁹⁴+1 = 4(0)₁₉₃1_<195> = 721324202162977116296517293557_<30> · C165
C165 = P36 · C130
P36 = 230366834312643340988031253121778481_<36>
C130 = [2407185357318598997321950360974409607977596627073563023341105908056951583447549498371976960901544198606857339244488454067274390253_<130>]

Apr 21, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁶-17)/3 = 1(6)₁₅₅1_<157> = 23 · 45530803605118052249663_<23> · C133
C133 = P43 · P90
P43 = 6980802854042367720418771014299511108668407_<43>
P90 = 227987074000655558378765635891409896833438917225088630429302578069324695128035262416578827_<90>

Number: n N=1591532816868544812411804196768146464448799537512375973859933367030542841491293027937220386483931368319354400599625525690188520018589 ( 133 digits) SNFS difficulty: 156 digits. Divisors found: r1=6980802854042367720418771014299511108668407 (pp43) r2=227987074000655558378765635891409896833438917225088630429302578069324695128035262416578827 (pp90) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 25.80 hours. Scaled time: 35.30 units (timescale=1.368). Factorization parameters were as follows: name: KA_1_6_155_1 n: 1591532816868544812411804196768146464448799537512375973859933367030542841491293027937220386483931368319354400599625525690188520018589 skew: 0.81 deg: 5 c5: 50 c0: -17 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:217226, largePrimes:6873287 encountered Relations: rels:6405229, finalFF:536584 Max relations in full relation-set: 28 Initial matrix: 434107 x 536584 with sparse part having weight 33216707. Pruned matrix : 344478 x 346712 with weight 17968311. Total sieving time: 23.46 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.06 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(34·10¹⁵⁵-7)/9 = 3(7)_155<156> = 1963259 · 15914463295100393_<17> · C134
C134 = P63 · P71
P63 = 614145112547407319622447176567788678504259865720750939348025889_<63>
P71 = 19687737655841001340058422437548321514709788974293541871489336377296939_<71>

Number: n N=12091127858450300921796173885173780987451322407445921454256127552779197749846655382931701572574680369104650104260662112804527612453771 ( 134 digits) SNFS difficulty: 156 digits. Divisors found: r1=614145112547407319622447176567788678504259865720750939348025889 (pp63) r2=19687737655841001340058422437548321514709788974293541871489336377296939 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.10 hours. Scaled time: 43.17 units (timescale=1.196). Factorization parameters were as follows: name: KA_3_7_155 n: 12091127858450300921796173885173780987451322407445921454256127552779197749846655382931701572574680369104650104260662112804527612453771 type: snfs skew: 0.73 deg: 5 c5: 34 c0: -7 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:216741, largePrimes:6612115 encountered Relations: rels:6128536, finalFF:545288 Max relations in full relation-set: 28 Initial matrix: 433623 x 545288 with sparse part having weight 31990210. Pruned matrix : 334870 x 337102 with weight 17003441. Total sieving time: 33.37 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.42 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 36.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 20, 2007 (3rd)

By Bos
10³⁰⁷+1 = 1(0)₃₀₆1_<308> = 11 · 3311436805543_<13> · 1490473286202873492575327109823_<31> · C264
C264 = P52 · C212
P52 = 5523722596446330977448218249241349336929189661174997_<52>
By Yousuke Koide / GMP-ECM / Apr 19, 2007
10⁷⁹⁹+1 = 1(0)₇₉₈1_<800> = 11 · 103 · 4013 · 6299 · 21993833369_<11> · 4855067598095567_<16> · 149419107039492234761_<21> · 297262705009139006771611927_<27> · C716
C716 = P31 · C686
P31 = 4588162642029183238011363957761_<31>
By Yousuke Koide / GMP-ECM / Apr 20, 2007
10⁸⁸⁹+1 = 1(0)₈₈₈1_<890> = 11 · 3557 · 909091 · 857772733 · 1094479651_<10> · 1125629957_<10> · 616896149073719728613_<21> · 4514666454616035926293_<22> · 10860110813777339731289_<23> · 52034716615139419063969613_<26> · 36099531273603138218699301565567581705151216702113889_<53> · C709
C709 = P31 · C679
P31 = 1515780514077670348158815644201_<31>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 20, 2007 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4 gnfs
(16·10²³⁵-61)/9 = 1(7)₂₃₄1_<236> = 11 · 29 · 37037719357719760261079_<23> · 386429589610739568586536276533_<30> · 713567298076051856522358950335091_<33> · 151909019354249419571440528481694434053_<39> · C110
C110 = P39 · P72
P39 = 125605990791686900936504691140588363699_<39>
P72 = 285985047765230062977841876142162519940065363490818809053547121928669731_<72>

Number: 17771_235 N=35921435276159625817527432090229298251807652677226377310650377800268125022879271309502187214950639477080494969 ( 110 digits) Divisors found: r1=125605990791686900936504691140588363699 (pp39) r2=285985047765230062977841876142162519940065363490818809053547121928669731 (pp72) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 41.18 hours. Scaled time: 24.75 units (timescale=0.601). Factorization parameters were as follows: name: 17771_235 n: 35921435276159625817527432090229298251807652677226377310650377800268125022879271309502187214950639477080494969 skew: 72976.38 # norm 1.70e+015 c5: 1260 c4: -836799224 c3: -25758351942273 c2: 3873905822348724057 c1: 36021861400424370105497 c0: -2749686868191143529867179949 # alpha -6.14 Y1: 46032740939 Y0: -1954330392375004368760 # Murphy_E 1.02e-009 # M 29519177398588835710920117477561627763408019706375126725127183876838642123095149601369374918428495280763074661 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2300001) Primes: RFBsize:230209, AFBsize:230179, largePrimes:7349364 encountered Relations: rels:7139629, finalFF:551314 Max relations in full relation-set: 28 Initial matrix: 460468 x 551314 with sparse part having weight 43597310. Pruned matrix : 383114 x 385480 with weight 25752079. Total sieving time: 31.84 hours. Total relation processing time: 0.46 hours. Matrix solve time: 8.38 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 41.18 hours. --------- CPU info (if available) ----------

Apr 20, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(25·10¹⁵⁵-7)/9 = 2(7)_155<156> = 17 · 402851 · 119336766838382837_<18> · C132
C132 = P31 · P101
P31 = 5881365932046077344716432736879_<31>
P101 = 57789862723272576198135690999645341036774247444723327437699375463079889097341640177561574510207039697_<101>

Number: n N=339883329838274876627404891772536715222229406033570353904935102531895001966367483580976478361229259406097110234232438139054308885663 ( 132 digits) SNFS difficulty: 156 digits. Divisors found: r1=5881365932046077344716432736879 (pp31) r2=57789862723272576198135690999645341036774247444723327437699375463079889097341640177561574510207039697 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 22.44 hours. Scaled time: 29.59 units (timescale=1.319). Factorization parameters were as follows: name: KA_2_7_155 n: 339883329838274876627404891772536715222229406033570353904935102531895001966367483580976478361229259406097110234232438139054308885663 skew: 0.78 deg: 5 c5: 25 c0: -7 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216906, largePrimes:6631137 encountered Relations: rels:6138516, finalFF:516545 Max relations in full relation-set: 48 Initial matrix: 433786 x 516545 with sparse part having weight 31142732. Pruned matrix : 360553 x 362785 with weight 16512544. Total sieving time: 19.62 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.53 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 22.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(61·10¹⁵⁵-7)/9 = 6(7)_155<156> = 103651 · 971857 · 19870534292309_<14> · C132
C132 = P43 · P89
P43 = 9817212608718080906317171875037375502190241_<43>
P89 = 34491630159507572267087764175508621104295293798871859880831023317096973793390053303999519_<89>

Number: n N=338611666497158570577221038924531523369668099643294585815227989598756413572175554597195188944774585124940329355800182760989710494079 ( 132 digits) SNFS difficulty: 156 digits. Divisors found: r1=9817212608718080906317171875037375502190241 (pp43) r2=34491630159507572267087764175508621104295293798871859880831023317096973793390053303999519 (pp89) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.00 hours. Scaled time: 36.23 units (timescale=1.449). Factorization parameters were as follows: name: KA_6_7_155 n: 338611666497158570577221038924531523369668099643294585815227989598756413572175554597195188944774585124940329355800182760989710494079 skew: 0.65 deg: 5 c5: 61 c0: -7 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:217077, largePrimes:6791757 encountered Relations: rels:6281039, finalFF:499165 Max relations in full relation-set: 28 Initial matrix: 433958 x 499165 with sparse part having weight 31139720. Pruned matrix : 377515 x 379748 with weight 19352078. Total sieving time: 21.80 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.97 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 19, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0, GGNFS-0.77.1-20060513-athlon-xp
(5·10¹⁵⁷-17)/3 = 1(6)₁₅₆1_<158> = 11 · 29 · 2757874996319_<13> · C143
C143 = P70 · P74
P70 = 1656783190595643799692672752239702194832989548613617120528492532923753_<70>
P74 = 11434516605064564778112562546194861690949907853799120239681553336330622717_<74>

Number: n N=18944514903857738707332591646436452068207141455181594958816450014272137613307196266921465281243223714647216073470199710589087367939471170696901 ( 143 digits) SNFS difficulty: 159 digits. Divisors found: r1=1656783190595643799692672752239702194832989548613617120528492532923753 (pp70) r2=11434516605064564778112562546194861690949907853799120239681553336330622717 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.71 hours. Scaled time: 34.64 units (timescale=1.297). Factorization parameters were as follows: name: KA_1_6_156_1 n: 18944514903857738707332591646436452068207141455181594958816450014272137613307196266921465281243223714647216073470199710589087367939471170696901 # skew: 0.51 # deg: 5 # c5: 500 # c0: -17 # m: 10000000000000000000000000000000 skew: 2.54 deg: 5 c5: 4 c0: -425 m: 50000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:215811, largePrimes:6744488 encountered Relations: rels:6227113, finalFF:502366 Max relations in full relation-set: 48 Initial matrix: 432691 x 502366 with sparse part having weight 33307367. Pruned matrix : 372729 x 374956 with weight 19077430. Total sieving time: 23.44 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.03 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 26.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(17·10¹⁵⁷-71)/9 = 1(8)₁₅₆1_<158> = 11 · 67 · 233 · 257 · 100133357531_<12> · C139
C139 = P34 · P50 · P56
P34 = 1974898746446825564654925588408067_<34>
P50 = 26084785568241325536093167306732883156016781297647_<50>
P56 = 82973420930499973861919069602007448123945832667668347767_<56>

Number: n N=2164343892835518454505300706637153514507175780157952502388586254372879429209130030340885911229358734804249 ( 106 digits) SNFS difficulty: 158 digits. Divisors found: r1=26084785568241325536093167306732883156016781297647 (pp50) r2=82973420930499973861919069602007448123945832667668347767 (pp56) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.74 hours. Scaled time: 45.71 units (timescale=1.440). Factorization parameters were as follows: name: KA_1_8_156_1 n: 2164343892835518454505300706637153514507175780157952502388586254372879429209130030340885911229358734804249 # n: 4274360040840707962086046706090075912461905742295530890501180085682533476011747446857603996863402993422314665552906852413675572058777476683 skew: 0.53 deg: 5 c5: 1700 c0: -71 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216847, largePrimes:6984289 encountered Relations: rels:6460078, finalFF:494384 Max relations in full relation-set: 28 Initial matrix: 433730 x 494384 with sparse part having weight 33551013. Pruned matrix : 384136 x 386368 with weight 22030613. Total sieving time: 27.98 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.49 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 31.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(10¹⁵⁵+11)/3 = (3)₁₅₄7_<155> = 37 · 56896144739519611259_<20> · C134
C134 = P66 · P68
P66 = 208670671770760497643092645164757469100993644951788309366799053839_<66>
P68 = 75880951367873792594180307042805485428254654408601835762623060247601_<68>

Number: n N=15834129096538631981876151311557857936639270420692829139295670131179001593315499680760105008976521203731578626121888596331739869590239 ( 134 digits) SNFS difficulty: 155 digits. Divisors found: r1=208670671770760497643092645164757469100993644951788309366799053839 (pp66) r2=75880951367873792594180307042805485428254654408601835762623060247601 (pp68) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 20.74 hours. Scaled time: 28.29 units (timescale=1.364). Factorization parameters were as follows: name: KA_3_154_7 n: 15834129096538631981876151311557857936639270420692829139295670131179001593315499680760105008976521203731578626121888596331739869590239 skew: 1.62 deg: 5 c5: 1 c0: 11 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:216816, AFBsize:216602, largePrimes:6531775 encountered Relations: rels:6070085, finalFF:530729 Max relations in full relation-set: 28 Initial matrix: 433482 x 530729 with sparse part having weight 30061199. Pruned matrix : 345492 x 347723 with weight 15473918. Total sieving time: 18.60 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.83 hours. Total square root time: 0.16 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 20.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 19, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=297500
(8·10¹⁵⁶-17)/9 = (8)₁₅₅7_<156> = 191413 · 294293 · 2247379721_<10> · C136
C136 = P31 · P106
P31 = 5289913621585527848874348853313_<31>
P106 = 1327306059679471772390175491604367168135356343238374722780556040926974678339394316436973392646103133527191_<106>
6·10¹⁵⁷+1 = 6(0)₁₅₆1_<158> = 83 · 151 · 72179234791_<11> · C143
C143 = P62 · P81
P62 = 72357737078330308558694680661590216271249223389638162975859539_<62>
P81 = 916640329258611436341178406620060063987449880780814068401233780150914565592579353_<81>

Number: n N=66326019939888731124137750913895090055834491742411539232321131200926135913206081132490874613518312074140366269836829752912617349628935239498267 ( 143 digits) SNFS difficulty: 157 digits. Divisors found: r1=72357737078330308558694680661590216271249223389638162975859539 (pp62) r2=916640329258611436341178406620060063987449880780814068401233780150914565592579353 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 34.58 hours. Scaled time: 41.32 units (timescale=1.195). Factorization parameters were as follows: name: KA_6_0_156_1 n: 66326019939888731124137750913895090055834491742411539232321131200926135913206081132490874613518312074140366269836829752912617349628935239498267 type: snfs skew: 0.28 deg: 5 c5: 600 c0: 1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:6418969 encountered Relations: rels:5891747, finalFF:502734 Max relations in full relation-set: 28 Initial matrix: 433818 x 502734 with sparse part having weight 28026248. Pruned matrix : 370197 x 372430 with weight 16844017. Total sieving time: 31.66 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.62 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 34.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁷-7)/3 = 1(3)₁₅₆1_<158> = 11² · 829048691 · C147
C147 = P43 · P51 · P54
P43 = 1298908648477793769569563217697406042467797_<43>
P51 = 227836378491183675155418024092575662345597837669647_<51>
P54 = 449129571882613139545490492415647300223051508767591019_<54>

Number: n N=132914795791607779393998246218504139069715027270851061093644960498598981368472560242293430048107688956563142563482955158125504335329938049244764521 ( 147 digits) SNFS difficulty: 157 digits. Divisors found: r1=1298908648477793769569563217697406042467797 (pp43) r2=227836378491183675155418024092575662345597837669647 (pp51) r3=449129571882613139545490492415647300223051508767591019 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.19 hours. Scaled time: 34.65 units (timescale=1.323). Factorization parameters were as follows: name: KA_1_3_156_1 n: 132914795791607779393998246218504139069715027270851061093644960498598981368472560242293430048107688956563142563482955158125504335329938049244764521 skew: 0.89 deg: 5 c5: 25 c0: -14 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:216976, largePrimes:6729179 encountered Relations: rels:6208493, finalFF:500339 Max relations in full relation-set: 48 Initial matrix: 433856 x 500339 with sparse part having weight 32743641. Pruned matrix : 376565 x 378798 with weight 19065606. Total sieving time: 22.56 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.26 hours. Total square root time: 0.19 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 26.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

2·10¹⁵⁷-1 = 1(9)_157<158> = 29 · 121465463101_<12> · C145
C145 = P36 · P46 · P63
P36 = 904379301033768345717044160825785309_<36>
P46 = 6457091006561228200494377454089107772956770149_<46>
P63 = 972280702625490682212362702573778085813248187465970804365743191_<63>

Number: n N=5677788194330897959207179477750316482872150625851073181155520400292142060208311316770349874503902856555645676417079579230816761535189098741201831 ( 145 digits) SNFS difficulty: 157 digits. Divisors found: r1=904379301033768345717044160825785309 (pp36) r2=6457091006561228200494377454089107772956770149 (pp46) r3=972280702625490682212362702573778085813248187465970804365743191 (pp63) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.26 hours. Scaled time: 36.63 units (timescale=1.450). Factorization parameters were as follows: name: KA_1_9_157 n: 5677788194330897959207179477750316482872150625851073181155520400292142060208311316770349874503902856555645676417079579230816761535189098741201831 skew: 0.35 deg: 5 c5: 200 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216391, largePrimes:6772954 encountered Relations: rels:6243826, finalFF:486214 Max relations in full relation-set: 28 Initial matrix: 433272 x 486214 with sparse part having weight 30147915. Pruned matrix : 387238 x 389468 with weight 19941665. Total sieving time: 21.50 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.35 hours. Total square root time: 0.23 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(34·10¹⁵⁷-43)/9 = 3(7)₁₅₆3_<158> = 3² · 11 · 19 · 199194337 · C147
C147 = P42 · P43 · P62
P42 = 173250819925329757405611840037528690186427_<42>
P43 = 9035055010084847015301845327796377263688437_<43>
P62 = 64411664896149439159157921804791266771402346028235778213017491_<62>

Number: n N=100825555763678864123952879910449161112867780638776593433396049472041667630761409311563611469958002535998500901578741834425443631381346614299281109 ( 147 digits) SNFS difficulty: 158 digits. Divisors found: r1=173250819925329757405611840037528690186427 (pp42) r2=9035055010084847015301845327796377263688437 (pp43) r3=64411664896149439159157921804791266771402346028235778213017491 (pp62) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 36.63 hours. Scaled time: 50.00 units (timescale=1.365). Factorization parameters were as follows: name: KA_3_7_156_3 n: 100825555763678864123952879910449161112867780638776593433396049472041667630761409311563611469958002535998500901578741834425443631381346614299281109 skew: 0.42 deg: 5 c5: 3400 c0: -43 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:216666, largePrimes:7082322 encountered Relations: rels:6565724, finalFF:496808 Max relations in full relation-set: 28 Initial matrix: 433549 x 496808 with sparse part having weight 35449720. Pruned matrix : 382013 x 384244 with weight 23549409. Total sieving time: 32.88 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.07 hours. Total square root time: 0.46 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 36.63 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 17, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(67·10¹⁵⁷+23)/9 = 7(4)₁₅₆7_<158> = 7 · 11 · 127 · 6967 · C151
C151 = P63 · P88
P63 = 196947610222755818047239895555064844541747218059447880546494957_<63>
P88 = 5548062197786922108597350799550470655831242112272889027561109789284452833290497739281647_<88>

Number: n N=1092677591221344731989402195062399694133774596337703177710456117434346634094828337879663080921205556013746255934117947275589207350751367595680888154179 ( 151 digits) SNFS difficulty: 158 digits. Divisors found: r1=196947610222755818047239895555064844541747218059447880546494957 (pp63) r2=5548062197786922108597350799550470655831242112272889027561109789284452833290497739281647 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.06 hours. Scaled time: 53.85 units (timescale=1.195). Factorization parameters were as follows: name: KA_7_4_156_7 n: 1092677591221344731989402195062399694133774596337703177710456117434346634094828337879663080921205556013746255934117947275589207350751367595680888154179 type: snfs skew: 0.32 deg: 5 c5: 6700 c0: 23 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:216816, AFBsize:217156, largePrimes:6920532 encountered Relations: rels:6425312, finalFF:546121 Max relations in full relation-set: 28 Initial matrix: 434039 x 546121 with sparse part having weight 33794146. Pruned matrix : 340986 x 343220 with weight 19013316. Total sieving time: 41.78 hours. Total relation processing time: 0.25 hours. Matrix solve time: 2.93 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 45.06 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 17, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=5000000
(16·10²³⁵-61)/9 = 1(7)₂₃₄1_<236> = 11 · 29 · 37037719357719760261079_<23> · 386429589610739568586536276533_<30> · 713567298076051856522358950335091_<33> · C148
C148 = P39 · C110
P39 = 151909019354249419571440528481694434053_<39>
C110 = [35921435276159625817527432090229298251807652677226377310650377800268125022879271309502187214950639477080494969_<110>]

Apr 17, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0
4·10¹⁵⁷+1 = 4(0)₁₅₆1_<158> = 1321757 · C152
C152 = P65 · P87
P65 = 46712194341161070054665870112933244096080435997557581817007450649_<65>
P87 = 647855429982898406721265781990638069224565341233236221727068040304877394852504476748157_<87>

Number: n N=30262748750337618790745954059634259549977794708104439772212290156208743362055203793132928367317139232097881834558091994216788713810481049088448179203893 ( 152 digits) SNFS difficulty: 157 digits. Divisors found: r1=46712194341161070054665870112933244096080435997557581817007450649 (pp65) r2=647855429982898406721265781990638069224565341233236221727068040304877394852504476748157 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.48 hours. Scaled time: 37.71 units (timescale=1.324). Factorization parameters were as follows: name: KA_4_0_156_1 n: 30262748750337618790745954059634259549977794708104439772212290156208743362055203793132928367317139232097881834558091994216788713810481049088448179203893 skew: 0.60 deg: 5 c5: 25 c0: 2 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216361, largePrimes:6961579 encountered Relations: rels:6487180, finalFF:542616 Max relations in full relation-set: 48 Initial matrix: 433241 x 542616 with sparse part having weight 39514323. Pruned matrix : 341666 x 343896 with weight 20499298. Total sieving time: 25.18 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.92 hours. Total square root time: 0.19 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(25·10¹⁵⁷-7)/9 = 2(7)_157<158> = 3 · 10521845651_<11> · C147
C147 = P31 · P39 · P79
P31 = 4362956850742075039517980258627_<31>
P39 = 100040644971784701090248442620273077603_<39>
P79 = 2016168926089972285768717434483905209452257464658912852672219715284978714326289_<79>
(22·10¹⁵⁷-1)/3 = 7(3)_157<158> = 19 · 673 · 10321 · C150
C150 = P42 · P109
P42 = 115927686658862052161466450041710948154663_<42>
P109 = 4793180825233510269061418780918265393286504290775973495713741172906980788176434671437734774907012714375415233_<109>

Number: n N=555662364806936210043869518444127395285863041941640292215664555985699685541322525073954809005319888749019410627569595884012866604527954705515730181479 ( 150 digits) SNFS difficulty: 158 digits. Divisors found: r1=115927686658862052161466450041710948154663 (pp42) r2=4793180825233510269061418780918265393286504290775973495713741172906980788176434671437734774907012714375415233 (pp109) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.30 hours. Scaled time: 38.12 units (timescale=1.449). Factorization parameters were as follows: name: KA_7_3_157 n: 555662364806936210043869518444127395285863041941640292215664555985699685541322525073954809005319888749019410627569595884012866604527954705515730181479 skew: 0.43 deg: 5 c5: 275 c0: -4 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216402, largePrimes:6807486 encountered Relations: rels:6293241, finalFF:497347 Max relations in full relation-set: 28 Initial matrix: 433285 x 497347 with sparse part having weight 31188309. Pruned matrix : 378686 x 380916 with weight 19580498. Total sieving time: 22.84 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.22 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 26.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 16, 2007 (4th)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000
9·10¹⁸²+1 = 9(0)₁₈₁1_<183> = 96497 · C178
C178 = P37 · C142
P37 = 6693857016013088704017026959632722629_<37>
C142 = [1393324476133628308508018984618709804986257885467422408615899381022222419474636732587515795416876689048777120508243524120001407382238214675677_<142>]

Apr 16, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
9·10¹⁵⁷+1 = 9(0)₁₅₆1_<158> = 7 · 13 · C156
C156 = P46 · P111
P46 = 2130403278394440947268336034474352786160213379_<46>
P111 = 464236512889873201316103265893901452919829671364175589843047024998926643175420109046920841497010559322144023409_<111>

Number: n N=989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011 ( 156 digits) SNFS difficulty: 157 digits. Divisors found: r1=2130403278394440947268336034474352786160213379 (pp46) r2=464236512889873201316103265893901452919829671364175589843047024998926643175420109046920841497010559322144023409 (pp111) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 28.69 hours. Scaled time: 39.18 units (timescale=1.366). Factorization parameters were as follows: name: KA_9_0_156_1 n: 989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011 skew: 0.26 deg: 5 c5: 900 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:215581, largePrimes:6978011 encountered Relations: rels:6516913, finalFF:544066 Max relations in full relation-set: 28 Initial matrix: 432461 x 544066 with sparse part having weight 35226913. Pruned matrix : 337254 x 339480 with weight 19166632. Total sieving time: 25.92 hours. Total relation processing time: 0.24 hours. Matrix solve time: 2.07 hours. Total square root time: 0.45 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 16, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(71·10¹⁷⁶-17)/9 = 7(8)₁₇₅7_<177> = C177
C177 = P38 · P40 · P101
P38 = 12444683223615891402820327212798136433_<38>
P40 = 3674375738140870081368352967131977691087_<40>
P101 = 17252356679429901956285793702431420438333359105122269293068907650150673519737446668316923181906393897_<101>

Number: 78887_176 N=788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 ( 177 digits) SNFS difficulty: 177 digits. Divisors found: r1=12444683223615891402820327212798136433 (pp38) r2=3674375738140870081368352967131977691087 (pp40) r3=17252356679429901956285793702431420438333359105122269293068907650150673519737446668316923181906393897 (pp101) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 853.40 hours. Scaled time: 520.57 units (timescale=0.610). Factorization parameters were as follows: name: 78887_176 n: 788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 100000000000000000000000000000000000 c5: 710 c0: -17 skew: 4 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 21600001 ) Primes: RFBsize:501962, AFBsize:500612, largePrimes:7104377 encountered Relations: rels:7627236, finalFF:1123512 Max relations in full relation-set: 0 Initial matrix: 1002641 x 1123512 with sparse part having weight 126171183. Pruned matrix : 914469 x 919546 with weight 104654058. Total sieving time: 754.46 hours. Total relation processing time: 2.84 hours. Matrix solve time: 95.54 hours. Time per square root: 0.56 hours. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 853.40 hours. --------- CPU info (if available) ----------

Apr 16, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0
5·10¹⁵⁷-1 = 4(9)_157<158> = 7 · 1784911 · 8397428359_<10> · C141
C141 = P54 · P88
P54 = 154950203473026832889059234829083441818646269399640511_<54>
P88 = 3075508559189988737150043030934655780723081191090507472552844326729132490697996382741663_<88>

Number: n N=476550677029524343665946953895574025260049383895835025193583187834239548403156077893198662913632520004443527829226385778591426880376782309793 ( 141 digits) SNFS difficulty: 159 digits. Divisors found: r1=154950203473026832889059234829083441818646269399640511 (pp54) r2=3075508559189988737150043030934655780723081191090507472552844326729132490697996382741663 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.22 hours. Scaled time: 43.28 units (timescale=1.195). Factorization parameters were as follows: name: KA_4_9_157 n: 476550677029524343665946953895574025260049383895835025193583187834239548403156077893198662913632520004443527829226385778591426880376782309793 type: snfs skew: 1.44 deg: 5 c5: 4 c0: -25 m: 50000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:216391, largePrimes:6478765 encountered Relations: rels:5936078, finalFF:494034 Max relations in full relation-set: 28 Initial matrix: 433271 x 494034 with sparse part having weight 27845713. Pruned matrix : 377954 x 380184 with weight 17470532. Total sieving time: 33.06 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.86 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 36.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

8·10¹⁵⁷-3 = 7(9)₁₅₆7_<158> = 7 · 11 · 17 · C155
C155 = P33 · P45 · P78
P33 = 483761069946232439153779120078097_<33>
P45 = 436213016886190495057964600551787363398983829_<45>
P78 = 289614834453526840832030464582741641059169146938996316648050252271982757768141_<78>

Number: n N=126333760671967568596793372125212909881306461592993045537085173685497608635758283948439567406499845534841917918495390391889 ( 123 digits) SNFS difficulty: 157 digits. Divisors found: r1=436213016886190495057964600551787363398983829 (pp45) r2=289614834453526840832030464582741641059169146938996316648050252271982757768141 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.82 hours. Scaled time: 31.43 units (timescale=1.440). Factorization parameters were as follows: name: KA_7_9_156_7 # n: 61115355233002291825821237585943468296409472880061115355233002291825821237585943468296409472880061115355233002291825821237585943468296409472880061115355233 n: 126333760671967568596793372125212909881306461592993045537085173685497608635758283948439567406499845534841917918495390391889 skew: 0.65 deg: 5 c5: 25 c0: -3 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216986, largePrimes:6644013 encountered Relations: rels:6128099, finalFF:494219 Max relations in full relation-set: 28 Initial matrix: 433866 x 494219 with sparse part having weight 28895318. Pruned matrix : 378977 x 381210 with weight 17891718. Total sieving time: 18.85 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.72 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 21.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 15, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁷+41)/9 = (4)₁₅₆9_<157> = 3 · 17 · 1777 · 2051898841117_<13> · C140
C140 = P69 · P71
P69 = 260221357440021455388738938889122776721896955085397138037228688252251_<69>
P71 = 91846157923309577470616859933689268561584874926674871536459883391952261_<71>

Number: n N=23900331890454200261779183585229763492153402399157688484259917920736681255730620727738466525300767323925829369751318965287932481166917789511 ( 140 digits) SNFS difficulty: 157 digits. Divisors found: r1=260221357440021455388738938889122776721896955085397138037228688252251 (pp69) r2=91846157923309577470616859933689268561584874926674871536459883391952261 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.44 hours. Scaled time: 44.13 units (timescale=1.450). Factorization parameters were as follows: name: KA_4_156_9 n: 23900331890454200261779183585229763492153402399157688484259917920736681255730620727738466525300767323925829369751318965287932481166917789511 skew: 1.27 deg: 5 c5: 25 c0: 82 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:217007, largePrimes:6992395 encountered Relations: rels:6471718, finalFF:493995 Max relations in full relation-set: 28 Initial matrix: 433887 x 493995 with sparse part having weight 33421745. Pruned matrix : 384649 x 386882 with weight 22052690. Total sieving time: 26.58 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.55 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 30.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(14·10¹⁵⁷-41)/9 = 1(5)₁₅₆1_<158> = 11 · 71 · 41893 · 4009117163_<10> · C141
C141 = P46 · P95
P46 = 1367055426296824724730956100096423270901258669_<46>
P95 = 86747738019244962078804322447103067350502553941506493682108511037049165854640129475050452781201_<95>

Number: n N=118588965978184191291589169425730928531988106038187106414487352675590392264054198803378536910232046817358432344625794912915634728702561481469 ( 141 digits) SNFS difficulty: 158 digits. Divisors found: r1=1367055426296824724730956100096423270901258669 (pp46) r2=86747738019244962078804322447103067350502553941506493682108511037049165854640129475050452781201 (pp95) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 30.51 hours. Scaled time: 41.55 units (timescale=1.362). Factorization parameters were as follows: name: KA_1_5_156_1 n: 118588965978184191291589169425730928531988106038187106414487352675590392264054198803378536910232046817358432344625794912915634728702561481469 skew: 0.49 deg: 5 c5: 1400 c0: -41 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216347, largePrimes:6833902 encountered Relations: rels:6305635, finalFF:490090 Max relations in full relation-set: 28 Initial matrix: 433230 x 490090 with sparse part having weight 31304275. Pruned matrix : 384277 x 386507 with weight 20392536. Total sieving time: 27.27 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.93 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 30.51 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(16·10¹⁵⁷-1)/3 = 5(3)_157<158> = 41 · 53 · C155
C155 = P39 · P117
P39 = 129797383107911921189114592848736731761_<39>
P117 = 189091960678640538527657346264288860676014584874491438046542017422669365733841635944493393437125375006515513942447561_<117>

Number: n N=24543641662831722656849210001533977603926982666053075625095873600245436416628317226568492100015339776039269826660530756250958736002454364166283172265684921 ( 155 digits) SNFS difficulty: 158 digits. Divisors found: r1=129797383107911921189114592848736731761 (pp39) r2=189091960678640538527657346264288860676014584874491438046542017422669365733841635944493393437125375006515513942447561 (pp117) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.92 hours. Scaled time: 33.95 units (timescale=1.310). Factorization parameters were as follows: name: KA_5_3_157 n: 24543641662831722656849210001533977603926982666053075625095873600245436416628317226568492100015339776039269826660530756250958736002454364166283172265684921 skew: 0.46 deg: 5 c5: 50 c0: -1 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:216926, largePrimes:6830845 encountered Relations: rels:6343658, finalFF:527782 Max relations in full relation-set: 48 Initial matrix: 433807 x 527782 with sparse part having weight 36099796. Pruned matrix : 353105 x 355338 with weight 19042809. Total sieving time: 22.85 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.82 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.92 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 14, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁶+41)/9 = (4)₁₅₅9_<156> = 35407 · 66888310787_<11> · C141
C141 = P43 · P98
P43 = 2320556509695116444764087997770288474407797_<43>
P98 = 80869726412245288072803531579541476425890112919981517500054469876923320277924027316762711210159313_<98>

Number: n N=187662770063198897254648711120578344957882722203045389305266787504281116290486371530577287601901816312256753988043095526936254851027699363461 ( 141 digits) SNFS difficulty: 156 digits. Divisors found: r1=2320556509695116444764087997770288474407797 (pp43) r2=80869726412245288072803531579541476425890112919981517500054469876923320277924027316762711210159313 (pp98) Version: GGNFS-0.77.1-20051202-athlon Total time: 38.23 hours. Scaled time: 50.65 units (timescale=1.325). Factorization parameters were as follows: name: KA_4_155_9 n: 187662770063198897254648711120578344957882722203045389305266787504281116290486371530577287601901816312256753988043095526936254851027699363461 skew: 1.00 deg: 5 c5: 40 c0: 41 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:216816, AFBsize:215452, largePrimes:7235441 encountered Relations: rels:6753303, finalFF:539005 Max relations in full relation-set: 48 Initial matrix: 432334 x 539005 with sparse part having weight 48979549. Pruned matrix : 350527 x 352752 with weight 27546472. Total sieving time: 33.84 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.08 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 38.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 14, 2007 (5th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
4·10¹⁹¹+1 = 4(0)₁₉₀1_<192> = 7 · 19 · 41 · 647 · 46903543 · 4164599914798824246547757_<25> · C153
C153 = P36 · P117
P36 = 765226605021062082766257793518013247_<36>
P117 = 758492370060731172732749892408126693839219951872236949815340112500285954615089467270693873387494136665940937734088263_<117>

Apr 14, 2007 (4th)

By Robert Backstrom / GMP-ECM 5.0 B1=624500, GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁷+1)/3 = 1(6)₁₅₆7_<158> = 398873142122850667_<18> · C140
C140 = P37 · P104
P37 = 2404393197926639638979396362008033281_<37>
P104 = 17378346996287391689755245493306607889153873952262426287646796171801225403604837211739059462503566941121_<104>
3·10¹⁵⁶-1 = 2(9)_156<157> = 23² · 757 · 37958325803_<11> · C140
C141 = P68 · P73
P68 = 34508927160252119290871470429799344288040408510935452205656946628557_<68>
P73 = 5719146168209700929932117892283471025039070385347664045593119483067546173_<73>

Number: n N=197361598537583584072731037228204834039638876801120022701727429667743993129175140505213658215476850235031414454539015439269856571655277862361 ( 141 digits) SNFS difficulty: 156 digits. Divisors found: r1=34508927160252119290871470429799344288040408510935452205656946628557 (pp68) r2=5719146168209700929932117892283471025039070385347664045593119483067546173 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.42 hours. Scaled time: 34.63 units (timescale=1.177). Factorization parameters were as follows: name: KA_2_9_156 n: 197361598537583584072731037228204834039638876801120022701727429667743993129175140505213658215476850235031414454539015439269856571655277862361 type: snfs skew: 0.51 deg: 5 c5: 30 c0: -1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:215581, largePrimes:6375624 encountered Relations: rels:5906725, finalFF:544951 Max relations in full relation-set: 28 Initial matrix: 432464 x 544951 with sparse part having weight 28722573. Pruned matrix : 329414 x 331640 with weight 14402843. Total sieving time: 27.08 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.98 hours. Total square root time: 0.15 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 29.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 14, 2007 (3rd)

By Alfred Reich / GMP-ECM B1=1000000, B1=250000
10¹⁴⁴³+1 = 1(0)₁₄₄₂1_<1444> = 7 · 11 · 13² · 157 · 223 · 859 · 2887 · 4663 · 6397 · 7253 · 158731 · 216451 · 1058313049_<10> · 1961853739_<10> · 78426117823_<11> · 388847808493_<12> · 126294442654927_<15> · 422650073734453_<15> · 1690016281413487_<16> · 296557347313446299_<18> · 5406655992229067083561_<22> · 21606064498691505246200058094681_<32> · 48911689110891303706174193415115219_<35> · C406 · C801
C801 = P32 · C779
P32 = 37344700192938647404842813656089_<32>
10¹⁷⁰⁹+1 = 1(0)₁₇₀₈1_<1710> = 11 · 6157019338133_<13> · C1696
C1696 = P34 · C1662
P34 = 5903378160150749077165810087494863_<34>
10¹⁸⁹²+1 = 1(0)₁₈₉₁1_<1893> = 73 · 137 · 617 · 1207097 · 7265281 · 1110411017_<10> · 277641151780258438310079109077611969_<36> · 2645778409917434965592366282025495569_<37> · 16205834846012967584927082656402106953_<38> · 38993135849791157061060738352944105076217_<41> · 34908493290773859017057784025792153817150916131843303273_<56> · C1659
C1659 = P25 · C1634
P25 = 2565225443270547964001657_<25>

Apr 14, 2007 (2nd)

By Yousuke Koide / GMP-ECM B1=1000000 / Apr 10, 2007
10⁷⁴³+1 = 1(0)₇₄₂1_<744> = 11 · 1487 · 8172691019111011124393086241_<28> · C711
C711 = P37 · C675
P37 = 2750793293893633690646483974559334689_<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 14, 2007

By Robert Backstrom /GGNFS-0.77.1-20060513-athlon-xp
(4·10¹⁵⁶+23)/9 = (4)₁₅₅7_<156> = 3 · 29 · 31 · 233 · 1162061 · C144
C144 = P60 · P84
P60 = 658237800790060433128895853813992111237171477712259462648973_<60>
P84 = 924631893046383441534389809744737352040680519541286830846552261752181915098853210999_<84>

Number: n N=608627663819201808417041980929346102662496861775520416798486790021398126579659692253604025739413646460016835809359875088363094393568287439654027 ( 144 digits) SNFS difficulty: 156 digits. Divisors found: r1=658237800790060433128895853813992111237171477712259462648973 (pp60) r2=924631893046383441534389809744737352040680519541286830846552261752181915098853210999 (pp84) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 33.77 hours. Scaled time: 46.16 units (timescale=1.367). Factorization parameters were as follows: name: KA_4_155_7 n: 608627663819201808417041980929346102662496861775520416798486790021398126579659692253604025739413646460016835809359875088363094393568287439654027 skew: 0.90 deg: 5 c5: 40 c0: 23 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2900001) Primes: RFBsize:216816, AFBsize:216736, largePrimes:7433946 encountered Relations: rels:6919180, finalFF:495297 Max relations in full relation-set: 28 Initial matrix: 433618 x 495297 with sparse part having weight 39970576. Pruned matrix : 400661 x 402893 with weight 28886141. Total sieving time: 29.38 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.80 hours. Total square root time: 0.42 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 33.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁶-41)/9 = (5)₁₅₅1_<156> = 31 · 97 · 2749 · 24137 · C145
C145 = P46 · P47 · P54
P46 = 1600207301265369924631020682960816113990739459_<46>
P47 = 16568556547968489324062487443384412430491937807_<47>
P54 = 105020749778702090985515156596077622754794211159073697_<54>

Number: n N=2784428283225929846214187821651575527617305853520025468536849587506685784217150177340144999173317301288623436378801171185958744655260831867158861 ( 145 digits) SNFS difficulty: 156 digits. Divisors found: r1=1600207301265369924631020682960816113990739459 (pp46) r2=16568556547968489324062487443384412430491937807 (pp47) r3=105020749778702090985515156596077622754794211159073697 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 34.15 hours. Scaled time: 40.63 units (timescale=1.190). Factorization parameters were as follows: name: KA_5_155_1 n: 2784428283225929846214187821651575527617305853520025468536849587506685784217150177340144999173317301288623436378801171185958744655260831867158861 type: snfs skew: 0.96 deg: 5 c5: 50 c0: -41 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1500000) Primes: RFBsize:216816, AFBsize:217342, largePrimes:6380461 encountered Relations: rels:5851563, finalFF:499097 Max relations in full relation-set: 28 Initial matrix: 434223 x 499097 with sparse part having weight 26951928. Pruned matrix : 373558 x 375793 with weight 16358185. Total sieving time: 30.79 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.65 hours. Total square root time: 0.49 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 34.15 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(52·10¹⁵⁶-7)/9 = 5(7)_156<157> = 219147336769_<12> · C146
C146 = P47 · P99
P47 = 43392867949703635301629857402687959159726060863_<47>
P99 = 607583935024911523260847922586741220802757668680390878600315487487290409913946585708438696721115791_<99>

Number: n N=26364809460897299259653125087975172032777393582242597341147785718166934780842624212004109229722134427960631940677808720415122325641908370536387633 ( 146 digits) SNFS difficulty: 158 digits. Divisors found: r1=43392867949703635301629857402687959159726060863 (pp47) r2=607583935024911523260847922586741220802757668680390878600315487487290409913946585708438696721115791 (pp99) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.15 hours. Scaled time: 47.79 units (timescale=1.322). Factorization parameters were as follows: name: KA_5_7_156 n: 26364809460897299259653125087975172032777393582242597341147785718166934780842624212004109229722134427960631940677808720415122325641908370536387633 skew: 0.84 deg: 5 c5: 65 c0: -28 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:217161, largePrimes:7027687 encountered Relations: rels:6501938, finalFF:500738 Max relations in full relation-set: 48 Initial matrix: 434044 x 500738 with sparse part having weight 41292245. Pruned matrix : 382040 x 384274 with weight 25445788. Total sieving time: 31.64 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.23 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 36.15 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(2·10¹⁵⁶-17)/3 = (6)₁₅₅1_<156> = 582040501417_<12> · C145
C145 = P57 · P88
P57 = 262422346638094064709676275686532663519430097478059007977_<57>
P88 = 4364703230483737983340490207355193123826831844937412896837700663993603235377768373454229_<88>

Number: n N=1145395664122412462028343745791750881390136369783276989631757880007432044155235692531185871687582370102016007875929567627122973983826576555384733 ( 145 digits) SNFS difficulty: 156 digits. Divisors found: r1=262422346638094064709676275686532663519430097478059007977 (pp57) r2=4364703230483737983340490207355193123826831844937412896837700663993603235377768373454229 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.89 hours. Scaled time: 41.65 units (timescale=1.442). Factorization parameters were as follows: name: KA_6_155_1 n: 1145395664122412462028343745791750881390136369783276989631757880007432044155235692531185871687582370102016007875929567627122973983826576555384733 skew: 0.97 deg: 5 c5: 20 c0: -17 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216481, largePrimes:7006733 encountered Relations: rels:6508602, finalFF:508486 Max relations in full relation-set: 28 Initial matrix: 433363 x 508486 with sparse part having weight 34854295. Pruned matrix : 370976 x 373206 with weight 21764226. Total sieving time: 25.33 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.31 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 12, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
(43·10¹⁵⁶-7)/9 = 4(7)_156<157> = 86036339801_<11> · C146
C146 = P38 · P109
P38 = 19163362490036635820158997010258849551_<38>
P109 = 2897826003981773784334186754550525299012182064741398699239307009312692916090017208342332671221035127546930327_<109>

Number: n N=55532090147357078614709045295335410496884507949289740354906265287483458384991574448553960954638656267233942947332864511635639261192072916572233177 ( 146 digits) SNFS difficulty: 157 digits. Divisors found: r1=19163362490036635820158997010258849551 (pp38) r2=2897826003981773784334186754550525299012182064741398699239307009312692916090017208342332671221035127546930327 (pp109) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.34 hours. Scaled time: 42.51 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_7_156 n: 55532090147357078614709045295335410496884507949289740354906265287483458384991574448553960954638656267233942947332864511635639261192072916572233177 skew: 0.44 deg: 5 c5: 430 c0: -7 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216651, largePrimes:6922881 encountered Relations: rels:6392211, finalFF:486337 Max relations in full relation-set: 28 Initial matrix: 433534 x 486337 with sparse part having weight 33091584. Pruned matrix : 388899 x 391130 with weight 22447641. Total sieving time: 25.47 hours. Total relation processing time: 0.26 hours. Matrix solve time: 3.53 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 29.34 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(31·10¹⁵⁶-13)/9 = 3(4)₁₅₅3_<157> = 4253 · 3873379 · C147
C147 = P47 · P101
P47 = 11446246509035109137458172315152085129446188827_<47>
P101 = 18267146564210168096334403162624796291792049909993727669100813582789777576039312403346776495047622407_<101>

Number: n N=209090262590623324674662272817826497803277807296152930210058551570312356683432041453306992533523096953980424674313366594580396798468355453918246589 ( 147 digits) SNFS difficulty: 157 digits. Divisors found: r1=11446246509035109137458172315152085129446188827 (pp47) r2=18267146564210168096334403162624796291792049909993727669100813582789777576039312403346776495047622407 (pp101) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 38.38 hours. Scaled time: 52.43 units (timescale=1.366). Factorization parameters were as follows: name: KA_3_4_155_3 n: 209090262590623324674662272817826497803277807296152930210058551570312356683432041453306992533523096953980424674313366594580396798468355453918246589 skew: 0.53 deg: 5 c5: 310 c0: -13 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 1300001) Primes: RFBsize:216816, AFBsize:216917, largePrimes:7085921 encountered Relations: rels:6631140, finalFF:560970 Max relations in full relation-set: 48 Initial matrix: 433800 x 560970 with sparse part having weight 45010433. Pruned matrix : 328753 x 330986 with weight 22946855. Total sieving time: 35.71 hours. Total relation processing time: 0.34 hours. Matrix solve time: 2.22 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 38.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 11, 2007 (4th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(4·10¹⁵⁸+41)/9 = (4)₁₅₇9_<158> = 7 · C157
C157 = P33 · P124
P33 = 707520375170029031923901699222657_<33>
P124 = 8973884812406325767083604587285833707833311930101241764893886063877897082565108219201301770248476197905635918804130248304151_<124>

Number: 44449_158 N=6349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207 ( 157 digits) SNFS difficulty: 158 digits. Divisors found: r1=707520375170029031923901699222657 (pp33) r2=8973884812406325767083604587285833707833311930101241764893886063877897082565108219201301770248476197905635918804130248304151 (pp124) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 71.54 hours. Scaled time: 48.29 units (timescale=0.675). Factorization parameters were as follows: name: 44449_158 n: 6349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207 m: 20000000000000000000000000000000 c5: 125 c0: 41 skew: 1 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:283743, largePrimes:5731791 encountered Relations: rels:5827031, finalFF:640293 Max relations in full relation-set: 0 Initial matrix: 566954 x 640293 with sparse part having weight 33663472. Pruned matrix : 507252 x 510150 with weight 25148829. Total sieving time: 61.49 hours. Total relation processing time: 0.49 hours. Matrix solve time: 9.35 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 71.54 hours. --------- CPU info (if available) ----------

Apr 11, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁶-13)/9 = (4)₁₅₅3_<156> = 467 · 907 · 4013 · C147
C147 = P71 · P76
P71 = 64377798252552010796638898829797497824812459415960828753897946965206549_<71>
P76 = 4061514751851283812525668056120841387861479610200189702623134793785876634331_<76>

Number: n N=261471377294445792783700915361605809384343473963181914540349510658242476460029162453106898744077559972780706732100864581694126371426615288359433719 ( 147 digits) SNFS difficulty: 156 digits. Divisors found: r1=64377798252552010796638898829797497824812459415960828753897946965206549 (pp71) r2=4061514751851283812525668056120841387861479610200189702623134793785876634331 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.69 hours. Scaled time: 37.95 units (timescale=1.323). Factorization parameters were as follows: name: KA_4_155_3 n: 261471377294445792783700915361605809384343473963181914540349510658242476460029162453106898744077559972780706732100864581694126371426615288359433719 skew: 0.80 deg: 5 c5: 40 c0: -13 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216811, largePrimes:7010544 encountered Relations: rels:6558496, finalFF:561592 Max relations in full relation-set: 48 Initial matrix: 433693 x 561592 with sparse part having weight 41536616. Pruned matrix : 326842 x 329074 with weight 20810724. Total sieving time: 25.66 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.76 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(89·10¹⁵⁶+1)/9 = 9(8)₁₅₅9_<157> = 23 · 173 · 3395911 · C147
C147 = P59 · P89
P59 = 35190907398243504644236934773128038169516636457174728867557_<59>
P89 = 20796334442362108455107590366458381110422317923673323714312825264926001029408728804836633_<89>

Number: n N=731841879584066931047543751234400010997014602921761226349534798267800406145405129532579566785063134021457398220721966959322822974289311948478815581 ( 147 digits) SNFS difficulty: 157 digits. Divisors found: r1=35190907398243504644236934773128038169516636457174728867557 (pp59) r2=20796334442362108455107590366458381110422317923673323714312825264926001029408728804836633 (pp89) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.30 hours. Scaled time: 42.22 units (timescale=1.196). Factorization parameters were as follows: name: KA_9_8_155_9 n: 731841879584066931047543751234400010997014602921761226349534798267800406145405129532579566785063134021457398220721966959322822974289311948478815581 type: snfs skew: 0.26 deg: 5 c5: 890 c0: 1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:217061, largePrimes:6420765 encountered Relations: rels:5891265, finalFF:498686 Max relations in full relation-set: 28 Initial matrix: 433944 x 498686 with sparse part having weight 28275743. Pruned matrix : 373550 x 375783 with weight 17348083. Total sieving time: 32.31 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.69 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 35.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 11, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs
3·10¹⁶²+1 = 3(0)₁₆₁1_<163> = 7130941393003213_<16> · 103809697153908617469853075665675511_<36> · C112
C112 = P43 · P70
P43 = 3853176322382181446159610642291595255342267_<43>
P70 = 1051762253929606176068974362696177686302006839768383025664246236931321_<70>

Number: 30001_162 N=4052625413616873991636843572634283505999285953539026570840954837694883840351540445126100833603885531257627444707 ( 112 digits) Divisors found: r1=3853176322382181446159610642291595255342267 (pp43) r2=1051762253929606176068974362696177686302006839768383025664246236931321 (pp70) Version: GGNFS-0.77.1-20050930-k8 Total time: 22.19 hours. Scaled time: 20.06 units (timescale=0.904). Factorization parameters were as follows: name: 30001_162 n: 4052625413616873991636843572634283505999285953539026570840954837694883840351540445126100833603885531257627444707 skew: 24998.54 # norm 8.26e+14 c5: 30720 c4: 13614228 c3: -60084665928514 c2: -116456741736186697 c1: 23483511012036749253564 c0: 202273762000039556636441520 # alpha -4.74 Y1: 33561962467 Y0: -2654990979919421104393 # Murphy_E 7.76e-10 # M 2153405058310236367653909476962872255556716105115408821461399974313824697223037807778680206665493728900569170632 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1400000, 2310001) Primes: RFBsize:203362, AFBsize:203526, largePrimes:7619804 encountered Relations: rels:7521013, finalFF:564629 Max relations in full relation-set: 28 Initial matrix: 406962 x 564629 with sparse part having weight 52440036. Pruned matrix : 295985 x 298083 with weight 30474900. Total sieving time: 21.10 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.81 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 22.19 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335815) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.10 BogoMIPS).

Apr 11, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
10¹⁵⁶-3 = (9)₁₅₅7_<156> = 47 · 193 · 123229 · C147
C147 = P39 · P45 · P65
P39 = 216167489536594248535065060052412135027_<39>
P45 = 272299045624505473727969700938204637516311713_<45>
P65 = 15198313925884879986745118948436722105397649149262271143998265333_<65>

Number: n N=894606210623443562437370687971114782906997814554858187251616555435460536420072344317247852347721206591645711492794592431809126919097277671344041583 ( 147 digits) SNFS difficulty: 156 digits. Divisors found: r1=216167489536594248535065060052412135027 (pp39) r2=272299045624505473727969700938204637516311713 (pp45) r3=15198313925884879986745118948436722105397649149262271143998265333 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.97 hours. Scaled time: 37.69 units (timescale=1.451). Factorization parameters were as follows: name: KA_9_155_7 n: 894606210623443562437370687971114782906997814554858187251616555435460536420072344317247852347721206591645711492794592431809126919097277671344041583 skew: 0.78 deg: 5 c5: 10 c0: -3 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216741, largePrimes:6968935 encountered Relations: rels:6496067, finalFF:534842 Max relations in full relation-set: 28 Initial matrix: 433623 x 534842 with sparse part having weight 36166595. Pruned matrix : 346951 x 349183 with weight 20208618. Total sieving time: 22.49 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.90 hours. Total square root time: 0.41 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.97 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 10, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(28·10¹⁵⁶+17)/9 = 3(1)₁₅₅3_<157> = 569 · 49207 · C150
C150 = P51 · P99
P51 = 258041949489809142594628345727012558270007587714629_<51>
P99 = 430611925331515945278355234075202645116773258228763345695469212454697948997089854505386842086459659_<99>

Number: n N=111115940686104503581856079641429811828289504979952561192074352342782581339735770340843425627146405295941295416701187016275354222042833472837412651511 ( 150 digits) SNFS difficulty: 158 digits. Divisors found: r1=258041949489809142594628345727012558270007587714629 (pp51) r2=430611925331515945278355234075202645116773258228763345695469212454697948997089854505386842086459659 (pp99) Version: GGNFS-0.77.1-20051202-athlon Total time: 44.65 hours. Scaled time: 18.48 units (timescale=0.414). Factorization parameters were as follows: name: KA_3_1_155_3 n: 111115940686104503581856079641429811828289504979952561192074352342782581339735770340843425627146405295941295416701187016275354222042833472837412651511 skew: 1.14 deg: 5 c5: 35 c0: 68 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216351, largePrimes:6885946 encountered Relations: rels:6345666, finalFF:487688 Max relations in full relation-set: 48 Initial matrix: 433234 x 487688 with sparse part having weight 35977625. Pruned matrix : 388722 x 390952 with weight 23183672. Total sieving time: 37.04 hours. Total relation processing time: 0.38 hours. Matrix solve time: 6.68 hours. Total square root time: 0.55 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 44.65 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

Apr 10, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
7·10¹⁴⁹+1 = 7(0)₁₄₈1_<150> = 353 · 4957 · 2883242209_<10> · C135
C135 = P41 · P94
P41 = 27592287833712963754580710491390334851359_<41>
P94 = 5028466680407615659824747536024164572850397380074196151582478698822339725661178413486182331051_<94>

Number: 70001_149 N=138746900008042067535370063618473556687052409299714471241482567692765626546602017744157274419812068105656310602659059177232164215248309 ( 135 digits) SNFS difficulty: 150 digits. Divisors found: r1=27592287833712963754580710491390334851359 (pp41) r2=5028466680407615659824747536024164572850397380074196151582478698822339725661178413486182331051 (pp94) Version: GGNFS-0.77.1-20050930-k8 Total time: 18.01 hours. Scaled time: 16.32 units (timescale=0.906). Factorization parameters were as follows: n: 138746900008042067535370063618473556687052409299714471241482567692765626546602017744157274419812068105656310602659059177232164215248309 m: 1000000000000000000000000000000 c5: 7 c0: 10 skew: 1.07 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176463, largePrimes:5488427 encountered Relations: rels:5366494, finalFF:447917 Max relations in full relation-set: 28 Initial matrix: 352830 x 447917 with sparse part having weight 39079032. Pruned matrix : 310526 x 312354 with weight 23800589. Total sieving time: 17.11 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.77 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 18.01 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.64 BogoMIPS (lpj=2335820) Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334232) Total of 2 processors activated (9340.10 BogoMIPS).

Apr 10, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
7·10¹⁵⁰+1 = 7(0)₁₄₉1_<151> = 12583 · 7011677 · 48703953167_<11> · C130
C130 = P57 · P73
P57 = 565102429506584132764175102442628047540137331998418471757_<57>
P73 = 2882707341673302681845839339823884543514446084956768454184275090583469569_<73>

Number: n N=1629024922336050068657788659269692317382596619897579011120619204318148940361751514344610856083178940847911436720610767527695462733 ( 130 digits) SNFS difficulty: 150 digits. Divisors found: r1=565102429506584132764175102442628047540137331998418471757 (pp57) r2=2882707341673302681845839339823884543514446084956768454184275090583469569 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 15.03 hours. Scaled time: 21.67 units (timescale=1.442). Factorization parameters were as follows: name: KA_7_0_149_1 n: 1629024922336050068657788659269692317382596619897579011120619204318148940361751514344610856083178940847911436720610767527695462733 skew: 0.68 deg: 5 c5: 7 c0: 1 m: 1000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:216816, AFBsize:216696, largePrimes:6671835 encountered Relations: rels:6397715, finalFF:678424 Max relations in full relation-set: 28 Initial matrix: 433579 x 678424 with sparse part having weight 37818009. Pruned matrix : 218215 x 220446 with weight 16835240. Total sieving time: 13.48 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.35 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 15.03 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

7·10¹⁴⁸+1 = 7(0)₁₄₇1_<149> = 3684925389750999011_<19> · C131
C131 = P47 · P84
P47 = 22029725720760974922384230516355618304117854041_<47>
P84 = 862303702875318574684178933529694530368164638218030948135135277879348224342523674051_<84>

Number: n N=18996314062339835051280977654167871538038033379285440954628687044055360698019796646292113856477734419790670423046806412629077190091 ( 131 digits) SNFS difficulty: 150 digits. Divisors found: r1=22029725720760974922384230516355618304117854041 (pp47) r2=862303702875318574684178933529694530368164638218030948135135277879348224342523674051 (pp84) Version: GGNFS-0.77.1-20051202-athlon Total time: 23.53 hours. Scaled time: 27.62 units (timescale=1.174). Factorization parameters were as follows: name: KA_7_0_147_1 n: 18996314062339835051280977654167871538038033379285440954628687044055360698019796646292113856477734419790670423046806412629077190091 type: snfs skew: 1.7 deg: 5 c5: 7 c0: 100 m: 1000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1000000) Primes: RFBsize:216816, AFBsize:216861, largePrimes:6027370 encountered Relations: rels:5537118, finalFF:521472 Max relations in full relation-set: 28 Initial matrix: 433744 x 521472 with sparse part having weight 22021191. Pruned matrix : 345863 x 348095 with weight 11418721. Total sieving time: 21.50 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.71 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 23.53 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(71·10¹⁵⁶-17)/9 = 7(8)₁₅₅7_<157> = 3 · 599 · 12277 · C150
C150 = P29 · P53 · P69
P29 = 31099767261536178071546920819_<29>
P53 = 36223816354507886781000373247374248840998059419011231_<53>
P69 = 317412601069020689414883025797217762217539557105881695471292639044507_<69>

Number: n N=357581882436031711187298212073967816854980617777699009036351023750130322227963174162910004582537732531280192848039016675810941946173440982402131437823 ( 150 digits) SNFS difficulty: 157 digits. Divisors found: r1=31099767261536178071546920819 (pp29) r2=36223816354507886781000373247374248840998059419011231 (pp53) r3=317412601069020689414883025797217762217539557105881695471292639044507 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 41.42 hours. Scaled time: 54.67 units (timescale=1.320). Factorization parameters were as follows: name: KA_7_8_155_7 n: 357581882436031711187298212073967816854980617777699009036351023750130322227963174162910004582537732531280192848039016675810941946173440982402131437823 skew: 0.47 deg: 5 c5: 710 c0: -17 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:216816, AFBsize:216537, largePrimes:7225880 encountered Relations: rels:6720908, finalFF:521001 Max relations in full relation-set: 48 Initial matrix: 433420 x 521001 with sparse part having weight 48206832. Pruned matrix : 366512 x 368743 with weight 28578075. Total sieving time: 36.36 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.66 hours. Total square root time: 0.17 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 41.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 9, 2007 (2nd)

By Alfred Reich / GMP-ECM B1=250000
10¹⁸³⁷+1 = 1(0)₁₈₃₆1_<1838> = 11² · 23 · 4093 · 8779 · 18371 · 84503 · 15849637 · 63716179 · 76272241 · 79402489 · 1657278943_<10> · 116011189311149998139_<21> · 272828068791212993437_<21> · 301525294918950432087520298129941558711551656822567015411_<57> · 14950128044255312629457887411604300692966728690551568705030373_<62> · C1619
C1619 = P27 · C1592
P27 = 562460722085835631233826201_<27>
10¹⁶⁶⁹+1 = 1(0)₁₆₆₈1_<1670> = 11 · 114715401881453_<15> · 534378091190893_<15> · C1640
C1640 = P28 · C1612
P28 = 1988409572496065915208771397_<28>
10¹⁷⁸⁶+1 = 1(0)₁₇₈₅1_<1787> = 101 · 45121 · 117640249 · 722817036322379041_<18> · 1369778187490592461_<19> · 2144906157509411684424913774078958939881_<40> · 1023037643093214557651333120422980213172396059301_<49> · C1648
C1648 = P28 · C1621
P28 = 2660633905954597855218572789_<28>

Apr 9, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(16·10¹⁵⁶-7)/9 = 1(7)_156<157> = 1528717 · C151
C151 = P69 · P82
P69 = 692135084257927329335410999683545165787859841786762908730251918987703_<69>
P82 = 1680194326615894932898979882414438056196314851519751157531292592032120525164197427_<82>

Number: n N=1162921441821983910545756852169353632999291417428979842428505588528012560714493119248217804719760281188590025346599650411278070288861691063668277240181 ( 151 digits) SNFS difficulty: 157 digits. Divisors found: r1=692135084257927329335410999683545165787859841786762908730251918987703 (pp69) r2=1680194326615894932898979882414438056196314851519751157531292592032120525164197427 (pp82) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.60 hours. Scaled time: 38.99 units (timescale=1.196). Factorization parameters were as follows: name: KA_1_7_156 n: 1162921441821983910545756852169353632999291417428979842428505588528012560714493119248217804719760281188590025346599650411278070288861691063668277240181 type: snfs skew: 1.07 deg: 5 c5: 5 c0: -7 m: 20000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216351, largePrimes:6344958 encountered Relations: rels:5824312, finalFF:504391 Max relations in full relation-set: 28 Initial matrix: 433232 x 504391 with sparse part having weight 26881004. Pruned matrix : 366674 x 368904 with weight 15845665. Total sieving time: 29.40 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.84 hours. Total square root time: 0.16 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 32.60 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(8·10¹⁵⁶-53)/9 = (8)₁₅₅3_<156> = 17 · 67 · 1723 · C150
C150 = P39 · P111
P39 = 512558391416894469920990361025843583071_<39>
P111 = 883680207797077854491786259675284953644239544020825359606312622673009480184253210227866307594638649702739828909_<111>

Number: n N=452937705835417271409275473485507946707123062551886137348943151958392236466546898613801136454674268999590261227858635650851384174798172373710068799539 ( 150 digits) SNFS difficulty: 157 digits. Divisors found: r1=512558391416894469920990361025843583071 (pp39) r2=883680207797077854491786259675284953644239544020825359606312622673009480184253210227866307594638649702739828909 (pp111) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.95 hours. Scaled time: 41.97 units (timescale=1.450). Factorization parameters were as follows: name: KA_8_155_3 n: 452937705835417271409275473485507946707123062551886137348943151958392236466546898613801136454674268999590261227858635650851384174798172373710068799539 skew: 1.84 deg: 5 c5: 5 c0: -106 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216631, largePrimes:6978351 encountered Relations: rels:6449777, finalFF:487734 Max relations in full relation-set: 28 Initial matrix: 433512 x 487734 with sparse part having weight 33253798. Pruned matrix : 388763 x 390994 with weight 22572948. Total sieving time: 24.84 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.85 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 8, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
9·10¹⁵⁶+1 = 9(0)₁₅₅1_<157> = 29 · C156
C156 = P39 · P40 · P77
P39 = 706993936910368903640116661982625450877_<39>
P40 = 8380009192709174113059633311180980138633_<40>
P77 = 52382271492126465895543889093087824425922340013871527868319133952371915809809_<77>

Number: n N=310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 ( 156 digits) SNFS difficulty: 158 digits. Divisors found: r1=706993936910368903640116661982625450877 (pp39) r2=8380009192709174113059633311180980138633 (pp40) r3=52382271492126465895543889093087824425922340013871527868319133952371915809809 (pp77) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.66 hours. Scaled time: 44.53 units (timescale=1.323). Factorization parameters were as follows: name: KA_9_0_155_1 n: 310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 skew: 1.22 deg: 5 c5: 10 c0: 27 m: 30000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216791, largePrimes:7067476 encountered Relations: rels:6585869, finalFF:536410 Max relations in full relation-set: 48 Initial matrix: 433674 x 536410 with sparse part having weight 43854241. Pruned matrix : 350813 x 353045 with weight 23765257. Total sieving time: 29.76 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.46 hours. Total square root time: 0.21 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 33.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(68·10¹⁵⁶+13)/9 = 7(5)₁₅₅7_<157> = 3 · 10891 · C153
C153 = P59 · P94
P59 = 31355131076919367852714514174234199910740419431555686047929_<59>
P94 = 7375114545207978805546688095481618474842984019533230866001850209009963716005668089754841511021_<94>

Number: n N=231247683272290746351897761318383850750024655083878295704574283217199386513499083511019972318292031816960657287532689240521395511754523782804014187725509 ( 153 digits) SNFS difficulty: 158 digits. Divisors found: r1=31355131076919367852714514174234199910740419431555686047929 (pp59) r2=7375114545207978805546688095481618474842984019533230866001850209009963716005668089754841511021 (pp94) Version: GGNFS-0.77.1-20051202-athlon Total time: 47.14 hours. Scaled time: 38.93 units (timescale=0.826). Factorization parameters were as follows: name: KA_7_5_155_7 n: 231247683272290746351897761318383850750024655083878295704574283217199386513499083511019972318292031816960657287532689240521395511754523782804014187725509 skew: 0.91 deg: 5 c5: 85 c0: 52 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [1500000, 1500000) Primes: RFBsize:216816, AFBsize:216711, largePrimes:7114301 encountered Relations: rels:6617701, finalFF:528432 Max relations in full relation-set: 28 Initial matrix: 433594 x 528432 with sparse part having weight 42665152. Pruned matrix : 357775 x 360006 with weight 24579218. Total sieving time: 42.61 hours. Total relation processing time: 0.41 hours. Matrix solve time: 3.98 hours. Total square root time: 0.14 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 47.14 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

Apr 8, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(7·10¹⁵⁴+11)/9 = (7)₁₅₃9_<154> = 3³ · 7337683 · C146
C146 = P61 · P85
P61 = 4690896086141897500802584645763269881758309040800801140340477_<61>
P85 = 8369066300074838263082780406544591031236656625018906009192714626063310059189782184047_<85>

Number: trial N=39258420351683109907409806377308183471730678056647106489618840664198654664521826615849423260912085866169540206093100999511586553239286882257770419 ( 146 digits) SNFS difficulty: 155 digits. Divisors found: r1=4690896086141897500802584645763269881758309040800801140340477 (pp61) r2=8369066300074838263082780406544591031236656625018906009192714626063310059189782184047 (pp85) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 84.95 hours. Scaled time: 45.45 units (timescale=0.535). Factorization parameters were as follows: n: 39258420351683109907409806377308183471730678056647106489618840664198654664521826615849423260912085866169540206093100999511586553239286882257770419 m: 10000000000000000000000000000000 c5: 7 c0: 110 skew: 1.73 type: snfsFactor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 1 ) Primes: RFBsize:216816, AFBsize:217222, largePrimes:5753913 encountered Relations: rels:5757438, finalFF:546532 Max relations in full relation-set: 0 Initial matrix: 434103 x 546532 with sparse part having weight 42400010. Pruned matrix : 403492 x 405726 with weight 24843896. Total sieving time: 77.64 hours. Total relation processing time: 0.62 hours. Matrix solve time: 6.39 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 84.95 hours. --------- CPU info (if available) ----------

Apr 7, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁵+13)/9 = (5)₁₅₄7_<155> = 3 · 107 · 197 · 3333804296728811_<16> · C135
C135 = P35 · P100
P35 = 41216820093313356609207852589825031_<35>
P100 = 6393543903130201756244045739931302422886188966077224891742387211909421803577183769409636962325124421_<100>

Number: n N=263521548814018004580209891831459686451851910557430681666590679838019891784536826927571192291545123292460712443696823152316035695182051 ( 135 digits) SNFS difficulty: 155 digits. Divisors found: r1=41216820093313356609207852589825031 (pp35) r2=6393543903130201756244045739931302422886188966077224891742387211909421803577183769409636962325124421 (pp100) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.43 hours. Scaled time: 32.98 units (timescale=1.297). Factorization parameters were as follows: name: KA_5_154_7 n: 263521548814018004580209891831459686451851910557430681666590679838019891784536826927571192291545123292460712443696823152316035695182051 skew: 1.21 deg: 5 c5: 5 c0: 13 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:217321, largePrimes:6770644 encountered Relations: rels:6260192, finalFF:509405 Max relations in full relation-set: 48 Initial matrix: 434202 x 509405 with sparse part having weight 33986023. Pruned matrix : 369089 x 371324 with weight 19110819. Total sieving time: 22.15 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.97 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(68·10¹⁵⁵+13)/9 = 7(5)₁₅₄7_<156> = 11 · 29 · 421 · 2475023 · 80018997103_<11> · C134
C134 = P48 · P86
P48 = 557831249566315798418346398963812640291677422857_<48>
P86 = 50923523018443023950549144339844652596348663112551716875431260247044827931812945961671_<86>

Number: n N=28406732477697117682136345726381636050128121431425594294290731080826521212711193096225911030485159627911792905855674723329202781314047 ( 134 digits) SNFS difficulty: 156 digits. Divisors found: r1=557831249566315798418346398963812640291677422857 (pp48) r2=50923523018443023950549144339844652596348663112551716875431260247044827931812945961671 (pp86) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.88 hours. Scaled time: 37.40 units (timescale=1.445). Factorization parameters were as follows: name: KA_7_5_154_7 n: 28406732477697117682136345726381636050128121431425594294290731080826521212711193096225911030485159627911792905855674723329202781314047 skew: 0.72 deg: 5 c5: 68 c0: 13 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:217331, largePrimes:6856703 encountered Relations: rels:6351061, finalFF:504197 Max relations in full relation-set: 28 Initial matrix: 434213 x 504197 with sparse part having weight 32033747. Pruned matrix : 373953 x 376188 with weight 19778157. Total sieving time: 22.57 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.07 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

9·10¹⁵⁰+1 = 9(0)₁₄₉1_<151> = 4253 · C148
C148 = P61 · P87
P61 = 3566992060520775519655367333427319075823880194840139594754009_<61>
P87 = 593259886101759296204495700498020412031125484426971874909743168024374007473423673233213_<87>

Number: n N=2116153303550434987067952033858452856806959793087232541735245708911356689395720667763931342581707030331530684222901481307312485304490947566423700917 ( 148 digits) SNFS difficulty: 150 digits. Divisors found: r1=3566992060520775519655367333427319075823880194840139594754009 (pp61) r2=593259886101759296204495700498020412031125484426971874909743168024374007473423673233213 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 20.35 hours. Scaled time: 24.33 units (timescale=1.196). Factorization parameters were as follows: name: KA_9_0_149_1 n: 2116153303550434987067952033858452856806959793087232541735245708911356689395720667763931342581707030331530684222901481307312485304490947566423700917 type: snfs skew: .64 deg: 5 c5: 9 c0: 1 m: 1000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:216816, AFBsize:216846, largePrimes:6003304 encountered Relations: rels:5565342, finalFF:557446 Max relations in full relation-set: 28 Initial matrix: 433726 x 557446 with sparse part having weight 22454058. Pruned matrix : 311345 x 313577 with weight 9852861. Total sieving time: 18.68 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.33 hours. Total square root time: 0.16 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 20.35 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

2·10¹⁵⁶-1 = 1(9)_156<157> = 31543 · C152
C152 = P32 · P120
P32 = 99879751314103257507070930078903_<32>
P120 = 634818460244410667590194554947948312452377489168571246831381943469948522781850559392697592627523228359592226813837713231_<120>

Number: n N=63405509938813682909044795992771771866975240148368893256824018007164822623085946168722061947183210220968202136765684938021114034809624956408711917065593 ( 152 digits) SNFS difficulty: 156 digits. Divisors found: r1=99879751314103257507070930078903 (pp32) r2=634818460244410667590194554947948312452377489168571246831381943469948522781850559392697592627523228359592226813837713231 (pp120) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.97 hours. Scaled time: 31.77 units (timescale=1.446). Factorization parameters were as follows: name: KA_1_9_156 n: 63405509938813682909044795992771771866975240148368893256824018007164822623085946168722061947183210220968202136765684938021114034809624956408711917065593 skew: 0.55 deg: 5 c5: 20 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216361, largePrimes:6725175 encountered Relations: rels:6222839, finalFF:505496 Max relations in full relation-set: 28 Initial matrix: 433243 x 505496 with sparse part having weight 30126514. Pruned matrix : 369600 x 371830 with weight 17843621. Total sieving time: 19.07 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.68 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 21.97 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 6, 2007 (7th)

By suberi / GMP-ECM 6.1.2 B1=3000000
(16·10¹⁵⁶-61)/9 = 1(7)₁₅₅1_<157> = 353 · 9320453 · 52622551337_<11> · 118052925097_<12> · C125
C125 = P40 · P86
P40 = 2966774020885178915193117624664369288559_<40>
P86 = 29317884310296032844640928591941378129027096529790688817039501129820426892441986873169_<86>

Apr 6, 2007 (6th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(2·10¹⁵⁷+61)/9 = (2)₁₅₆9_<157> = 3 · C156
C156 = P70 · P87
P70 = 2124001047704260764969871594481033371460532700579941038302624662161929_<70>
P87 = 348747822672392181906445498167694063047435422994624510314413787974685333027581184663567_<87>

Number: 22229_157 N=740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 ( 156 digits) SNFS difficulty: 157 digits. Divisors found: r1=2124001047704260764969871594481033371460532700579941038302624662161929 (pp70) r2=348747822672392181906445498167694063047435422994624510314413787974685333027581184663567 (pp87) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 62.82 hours. Scaled time: 42.34 units (timescale=0.674). Factorization parameters were as follows: name: 22229_157 n: 740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 m: 10000000000000000000000000000000 c5: 200 c0: 61 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:216677, largePrimes:5625784 encountered Relations: rels:5541384, finalFF:486522 Max relations in full relation-set: 0 Initial matrix: 433558 x 486522 with sparse part having weight 37329396. Pruned matrix : 410517 x 412748 with weight 28627425. Total sieving time: 54.70 hours. Total relation processing time: 0.49 hours. Matrix solve time: 7.44 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 62.82 hours. --------- CPU info (if available) ----------

Apr 6, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(85·10¹⁵⁵+41)/9 = 9(4)₁₅₄9_<156> = 11 · 541 · 12918769 · C146
C146 = P42 · P48 · P57
P42 = 211700555063119929890875235473012007515787_<42>
P48 = 168922285910824157078507837032846030320795260327_<48>
P57 = 343523448472478512600512197801355359657515353958015774379_<57>

Number: n N=12284722009921359929131917984001874509741121627632771385728056425443589682952011109511750289812874167807618558883312054960486639823425788913136271 ( 146 digits) SNFS difficulty: 156 digits. Divisors found: r1=211700555063119929890875235473012007515787 (pp42) r2=168922285910824157078507837032846030320795260327 (pp48) r3=343523448472478512600512197801355359657515353958015774379 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.63 hours. Scaled time: 39.03 units (timescale=1.196). Factorization parameters were as follows: name: KA_9_4_154_9 n: 12284722009921359929131917984001874509741121627632771385728056425443589682952011109511750289812874167807618558883312054960486639823425788913136271 type: snfs skew: 1 deg: 5 c5: 85 c0: 41 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216987, largePrimes:6273146 encountered Relations: rels:5738314, finalFF:489456 Max relations in full relation-set: 28 Initial matrix: 433869 x 489456 with sparse part having weight 25703479. Pruned matrix : 380465 x 382698 with weight 16215397. Total sieving time: 29.29 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.69 hours. Total square root time: 0.41 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 32.63 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

9·10¹⁴¹+1 = 9(0)₁₄₀1_<142> = 66031908616111316843093170997_<29> · C114
C114 = P35 · P80
P35 = 10183815601095370522960916473439173_<35>
P80 = 13383759748561580248834032773181350478449614572726727955728581327175944905132921_<80>

Number: n N=136297741328713674413693066891690669437698508191359111723956358226887622689098652320651044431037249295329573314333 ( 114 digits) SNFS difficulty: 143 digits. Divisors found: r1=10183815601095370522960916473439173 (pp35) r2=13383759748561580248834032773181350478449614572726727955728581327175944905132921 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.33 hours. Scaled time: 9.37 units (timescale=0.827). Factorization parameters were as follows: name: KA_9_0_140_1 n: 136297741328713674413693066891690669437698508191359111723956358226887622689098652320651044431037249295329573314333 skew: 1.22 deg: 5 c5: 10 c0: 27 m: 30000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:183066, largePrimes:6647249 encountered Relations: rels:6179370, finalFF:529120 Max relations in full relation-set: 48 Initial matrix: 366205 x 529120 with sparse part having weight 32879271. Pruned matrix : 228116 x 230011 with weight 13740621. Total sieving time: 9.36 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.59 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 11.33 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

Apr 6, 2007 (4th)

By Jo Yeong Uk / GMP-ECM 5.0.3 B1=3000000, GGNFS-0.77.1-20050930-k8
9·10¹⁶⁰+1 = 9(0)₁₅₉1_<161> = C161
C161 = P42 · C120
P42 = 196668336511615844317373683402996797341833_<42>
C120 = [457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497_<120>]
9·10¹⁴²+1 = 9(0)₁₄₁1_<143> = 229133 · C138
C138 = P39 · P100
P39 = 310418237090102149002920451352517921093_<39>
P100 = 1265341173550541325953165241360932050982648906067589633583866154278345401523423025383948873896217729_<100>

Number: 90001_142 N=392784976411080027756804999716321961480886646620085277982656361152692977441049521456970405834166182959242012281076929119768867862769657797 ( 138 digits) SNFS difficulty: 142 digits. Divisors found: r1=310418237090102149002920451352517921093 (pp39) r2=1265341173550541325953165241360932050982648906067589633583866154278345401523423025383948873896217729 (pp100) Version: GGNFS-0.77.1-20050930-k8 Total time: 9.89 hours. Scaled time: 8.98 units (timescale=0.908). Factorization parameters were as follows: n: 392784976411080027756804999716321961480886646620085277982656361152692977441049521456970405834166182959242012281076929119768867862769657797 m: 10000000000000000000000000000 c5: 900 c0: 1 skew: 1 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1300001) Primes: RFBsize:114155, AFBsize:113802, largePrimes:2682733 encountered Relations: rels:2690141, finalFF:314070 Max relations in full relation-set: 28 Initial matrix: 228021 x 314070 with sparse part having weight 20532393. Pruned matrix : 190077 x 191281 with weight 10216464. Total sieving time: 9.68 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 9.89 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

7·10¹⁶⁸+1 = 7(0)₁₆₇1_<169> = C169
C169 = P32 · P138
P32 = 39874420514155621405930029196213_<32>
P138 = 175551140549239192504522004124894766597610705708295751211644739831183679452961360088433039867758405935282447575807483052676447787480773277_<138>

Apr 6, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
9·10¹³⁹+1 = 9(0)₁₃₈1_<140> = 7 · 13² · 59 · 4424608127_<10> · C126
C126 = P38 · P41 · P47
P38 = 78922087410589632675170017604509175183_<38>
P41 = 80446991336116621276555908785459354423609_<41>
P47 = 45901044757666544367296133139543971866289750757_<47>

Number: 90001_139 N=291427774943488532047152968430812186544474227918461927420354897872451236915447049045959903935550375259390389351446759644503379 ( 126 digits) SNFS difficulty: 140 digits. Divisors found: r1=78922087410589632675170017604509175183 (pp38) r2=80446991336116621276555908785459354423609 (pp41) r3=45901044757666544367296133139543971866289750757 (pp47) Version: GGNFS-0.77.1-20050930-k8 Total time: 7.37 hours. Scaled time: 6.69 units (timescale=0.908). Factorization parameters were as follows: n: 291427774943488532047152968430812186544474227918461927420354897872451236915447049045959903935550375259390389351446759644503379 m: 10000000000000000000000000000 c5: 9 c0: 10 skew: 1.02 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114347, largePrimes:2606524 encountered Relations: rels:2587319, finalFF:291732 Max relations in full relation-set: 28 Initial matrix: 228566 x 291732 with sparse part having weight 17521246. Pruned matrix : 192093 x 193299 with weight 9457557. Total sieving time: 7.17 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 7.37 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 6, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(7·10¹⁵⁵-1)/3 = 2(3)_155<156> = 23 · 179 · 2130837571_<10> · C143
C143 = P68 · P75
P68 = 77461896204587304692802549568692094784149038435678059800315429975651_<68>
P75 = 343366126043325324679343651655973979954780461786276458351742207522660246169_<75>

Number: n N=26597791215739308044490594222247537267372861584429149293061049124427324190079794935545891769979405882539329762729960567612604616679833336031019 ( 143 digits) SNFS difficulty: 155 digits. Divisors found: r1=77461896204587304692802549568692094784149038435678059800315429975651 (pp68) r2=343366126043325324679343651655973979954780461786276458351742207522660246169 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.30 hours. Scaled time: 23.40 units (timescale=0.827). Factorization parameters were as follows: name: KA_2_3_155 n: 26597791215739308044490594222247537267372861584429149293061049124427324190079794935545891769979405882539329762729960567612604616679833336031019 skew: 1 deg: 5 c5: 7 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:216816, AFBsize:216696, largePrimes:6565054 encountered Relations: rels:6066011, finalFF:508144 Max relations in full relation-set: 48 Initial matrix: 433579 x 508144 with sparse part having weight 30474705. Pruned matrix : 365661 x 367892 with weight 17059396. Total sieving time: 24.44 hours. Total relation processing time: 0.32 hours. Matrix solve time: 3.44 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.30 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

Apr 6, 2007

By Philippe STROHL / GGNFS-0.77.1-20060722-pentium-m
(7·10¹⁷⁵+11)/9 = (7)₁₇₄9_<175> = 3 · 506195919767_<12> · 18822712509076627_<17> · 12007442890556404705517171537299_<32> · C116
C116 = P36 · P80
P36 = 498624942550109485805814460298361641_<36>
P80 = 45447384816690114799306728579382713054661212062218116456521891841090634833086503_<80>

Apr 5, 2007 (8th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁵-17)/3 = 1(6)₁₅₄1_<156> = 11 · 61 · 10061 · 10351541267_<11> · C139
C139 = P64 · P76
P64 = 1850217218604904705518625678066942001084019396417929806014990607_<64>
P76 = 1289013139523539875414561025232330466630448746167402715567364053956199454099_<76>

Number: n N=2384954305754419907374721739212565653128503425209626432308736488438207987809067828309162718996422968888385930009018811111685156024012648093 ( 139 digits) SNFS difficulty: 155 digits. Divisors found: r1=1850217218604904705518625678066942001084019396417929806014990607 (pp64) r2=1289013139523539875414561025232330466630448746167402715567364053956199454099 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.79 hours. Scaled time: 25.77 units (timescale=1.302). Factorization parameters were as follows: name: KA_1_6_154_1 n: 2384954305754419907374721739212565653128503425209626432308736488438207987809067828309162718996422968888385930009018811111685156024012648093 skew: 1.28 deg: 5 c5: 5 c0: -17 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:216816, AFBsize:216751, largePrimes:6454719 encountered Relations: rels:5971797, finalFF:513567 Max relations in full relation-set: 48 Initial matrix: 433632 x 513567 with sparse part having weight 28449479. Pruned matrix : 359396 x 361628 with weight 15123330. Total sieving time: 17.30 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.27 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 19.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

9·10¹⁵¹+1 = 9(0)₁₅₀1_<152> = 7 · 13 · 157 · C148
C148 = P37 · P55 · P57
P37 = 1740270742464737399801648274260382251_<37>
P55 = 6819290242424764524862346427986183895917940998262231863_<55>
P57 = 530817791290284114816038893859259470090732398434626858971_<57>

Number: n N=6299433051025407713305802477777000069993700566948974592286694197522222999930006299433051025407713305802477777000069993700566948974592286694197522223 ( 148 digits) SNFS difficulty: 153 digits. Divisors found: r1=1740270742464737399801648274260382251 (pp37) r2=6819290242424764524862346427986183895917940998262231863 (pp55) r3=530817791290284114816038893859259470090732398434626858971 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 18.56 hours. Scaled time: 26.73 units (timescale=1.440). Factorization parameters were as follows: name: KA_9_0_150_1 n: 6299433051025407713305802477777000069993700566948974592286694197522222999930006299433051025407713305802477777000069993700566948974592286694197522223 skew: 1.22 deg: 5 c5: 10 c0: 27 m: 3000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 850001) Primes: RFBsize:183072, AFBsize:183066, largePrimes:6485918 encountered Relations: rels:5920454, finalFF:416460 Max relations in full relation-set: 28 Initial matrix: 366205 x 416460 with sparse part having weight 28593043. Pruned matrix : 325166 x 327061 with weight 18726059. Total sieving time: 16.07 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.24 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 18.56 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 5, 2007 (7th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
9·10¹³⁷+1 = 9(0)₁₃₆1_<138> = 12487 · C134
C134 = P30 · P38 · P67
P30 = 499844315469822755436751497077_<30>
P38 = 22694932497912076567821810183311352533_<38>
P67 = 6353612804509099688291593709903803564908420180194675150217717604303_<67>

Number: 90001_137 N=72074957956274525506526787859373748698646592456154400576599663650196204052214302874989989589172739649235204612797309201569632417714423 ( 134 digits) SNFS difficulty: 137 digits. Divisors found: r1=499844315469822755436751497077 (pp30) r2=22694932497912076567821810183311352533 (pp38) r3=6353612804509099688291593709903803564908420180194675150217717604303 (pp67) Version: GGNFS-0.77.1-20050930-k8 Total time: 6.82 hours. Scaled time: 6.18 units (timescale=0.905). Factorization parameters were as follows: n: 72074957956274525506526787859373748698646592456154400576599663650196204052214302874989989589172739649235204612797309201569632417714423 m: 1000000000000000000000000000 c5: 900 c0: 1 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [650000, 1700001) Primes: RFBsize:100021, AFBsize:99793, largePrimes:1621648 encountered Relations: rels:1655072, finalFF:231349 Max relations in full relation-set: 28 Initial matrix: 199878 x 231349 with sparse part having weight 11731570. Pruned matrix : 185095 x 186158 with weight 8027989. Total sieving time: 6.66 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000 total time: 6.82 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 5, 2007 (6th)

By Alfred Reich / GMP-ECM B1=150000
10¹⁸²³+1 = 1(0)₁₈₂₂1_<1824> = 11 · 1187345615675521_<16> · C1807
C1807 = P26 · C1782
P26 = 31955183441582314302903853_<26>
10¹⁹⁴³+1 = 1(0)₁₉₄₂1_<1944> = 11 · 59 · 8685211 · 182142902141813_<15> · 154083204930662557781201849_<27> · 909090909090909090909090909090909090909090909090909090909090909091_<66> · C1827
C1827 = P27 · C1801
P27 = 549079354489571267845038917_<27>

Apr 5, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
7·10¹⁴⁷+1 = 7(0)₁₄₆1_<148> = 283183 · 1902961 · 4224729381223999559_<19> · C118
C118 = P43 · P76
P43 = 1257698080821893649965656268769551561386291_<43>
P76 = 2444700608743657571446769617615111125524512245960929287873490693266909697683_<76>

Number: 70001_147 N=3074695263801013246179651465377774841536765090589909013606376195809919254938620808513180930889035167934758547190663753 ( 118 digits) SNFS difficulty: 147 digits. Divisors found: r1=1257698080821893649965656268769551561386291 (pp43) r2=2444700608743657571446769617615111125524512245960929287873490693266909697683 (pp76) Version: GGNFS-0.77.1-20050930-k8 Total time: 15.32 hours. Scaled time: 13.88 units (timescale=0.906). Factorization parameters were as follows: n: 3074695263801013246179651465377774841536765090589909013606376195809919254938620808513180930889035167934758547190663753 m: 100000000000000000000000000000 c5: 700 c0: 1 skew: 1 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [900000, 1725001) Primes: RFBsize:135072, AFBsize:134603, largePrimes:2749251 encountered Relations: rels:2756068, finalFF:334962 Max relations in full relation-set: 28 Initial matrix: 269742 x 334962 with sparse part having weight 19110574. Pruned matrix : 236626 x 238038 with weight 11511077. Total sieving time: 15.00 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.24 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000 total time: 15.32 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

9·10¹¹⁸+1 = 9(0)₁₁₇1_<119> = 196073 · C114
C114 = P33 · P40 · P43
P33 = 186381179361616798004946995918881_<33>
P40 = 1741085366837536144261031347273683656221_<40>
P43 = 1414498837021419722168181729011819304044237_<43>

Number: 90001_118 N=459012714652195865825483365889235131813151224288912802884639904525355352343259908299459895039092582864545347906137 ( 114 digits) SNFS difficulty: 118 digits. Divisors found: r1=186381179361616798004946995918881 (pp33) r2=1741085366837536144261031347273683656221 (pp40) r3=1414498837021419722168181729011819304044237 (pp43) Version: GGNFS-0.77.1-20050930-k8 Total time: 1.71 hours. Scaled time: 1.55 units (timescale=0.903). Factorization parameters were as follows: n: 459012714652195865825483365889235131813151224288912802884639904525355352343259908299459895039092582864545347906137 m: 100000000000000000000000000000 c4: 900 c0: 1 skew: 1 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 625001) Primes: RFBsize:56543, AFBsize:56367, largePrimes:1979349 encountered Relations: rels:1930833, finalFF:130207 Max relations in full relation-set: 28 Initial matrix: 112979 x 130207 with sparse part having weight 10923724. Pruned matrix : 108529 x 109157 with weight 7699852. Total sieving time: 1.63 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,118,4,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,25000 total time: 1.71 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

9·10¹³⁰+1 = 9(0)₁₂₉1_<131> = 17 · 24593 · C126
C126 = P33 · P93
P33 = 216594009296418960195645951195437_<33>
P93 = 993883859583954448735204608842181266122491024424875540660278630042828155798346154067493353733_<93>

Number: 90001_130 N=215269289922287786338054109131962466603361549556186480610216680499711778339604048019402938664995539141936610369760883656516321 ( 126 digits) SNFS difficulty: 130 digits. Divisors found: r1=216594009296418960195645951195437 (pp33) r2=993883859583954448735204608842181266122491024424875540660278630042828155798346154067493353733 (pp93) Version: GGNFS-0.77.1-20050930-k8 Total time: 2.48 hours. Scaled time: 2.26 units (timescale=0.909). Factorization parameters were as follows: n: 215269289922287786338054109131962466603361549556186480610216680499711778339604048019402938664995539141936610369760883656516321 m: 100000000000000000000000000 c5: 9 c0: 1 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78476, largePrimes:1520791 encountered Relations: rels:1555753, finalFF:208863 Max relations in full relation-set: 28 Initial matrix: 157038 x 208863 with sparse part having weight 10306656. Pruned matrix : 132322 x 133171 with weight 5117766. Total sieving time: 2.41 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,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.48 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 5, 2007 (4th)

By Shaopu Lin / GGNFS-0.77.1-20060722-pentium4
9·10¹¹⁵+1 = 9(0)₁₁₄1_<116> = 7 · 13 · 103 · 3391343 · 4528368424529_<13> · C93
C93 = P35 · P59
P35 = 40963716780981360581121590745000013_<35>
P59 = 15263392336091573406619034605037192244798168990720053726167_<59>

Number: 9.115.+1 N=625245280772656676746155571910659372750816392845660093458760975741039193818228550885113440171 ( 93 digits) SNFS difficulty: 115 digits. Divisors found: r1=40963716780981360581121590745000013 (pp35) r2=15263392336091573406619034605037192244798168990720053726167 (pp59) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 1.71 hours. Scaled time: 2.14 units (timescale=1.248). Factorization parameters were as follows: n: 625245280772656676746155571910659372750816392845660093458760975741039193818228550885113440171 m: 100000000000000000000000 c5: 9 c0: 1 skew: 0.6443940149772542505082929811 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:64013, largePrimes:2156403 encountered Relations: rels:2356568, finalFF:351185 Max relations in full relation-set: 32 Initial matrix: 113175 x 351185 with sparse part having weight 28702487. Pruned matrix : 67902 x 68531 with weight 4049822. Total sieving time: 1.55 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.71 hours. --------- CPU info (if available) ----------

9·10¹⁰⁶+1 = 9(0)₁₀₅1_<107> = 53 · 109 · 601 · C101
C101 = P36 · P65
P36 = 273608402981042587412878642296398297_<36>
P65 = 94740623536944631063360702956769539501899999853290343142238204929_<65>

Number: 9.106.+1 N=25921830703371594915519313636006229303938361342831476130170217141415395320879141768508259127292605913 ( 101 digits) SNFS difficulty: 106 digits. Divisors found: r1=273608402981042587412878642296398297 (pp36) r2=94740623536944631063360702956769539501899999853290343142238204929 (pp65) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 1.31 hours. Scaled time: 1.64 units (timescale=1.253). Factorization parameters were as follows: n: 25921830703371594915519313636006229303938361342831476130170217141415395320879141768508259127292605913 m: 1000000000000000000000 c5: 90 c0: 1 skew: 0.4065851364889782182814046414 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 450001) Primes: RFBsize:49098, AFBsize:64158, largePrimes:1914669 encountered Relations: rels:1900606, finalFF:178309 Max relations in full relation-set: 32 Initial matrix: 113323 x 178309 with sparse part having weight 12518519. Pruned matrix : 87858 x 88488 with weight 3836011. Total sieving time: 1.14 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.06 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.31 hours. --------- CPU info (if available) ----------

9·10¹²⁰+1 = 9(0)₁₁₉1_<121> = 261066330188528555113_<21> · C101
C101 = P36 · P66
P36 = 177543491136813067537023060576498121_<36>
P66 = 194172127768048952704457311156481550648638322505777201579412750737_<66>

Number: 9.120.+1 N=34473997445402733752180794441478216709139205993978969681670845367942169957821117137970678303321865177 ( 101 digits) SNFS difficulty: 120 digits. Divisors found: r1=177543491136813067537023060576498121 (pp36) r2=194172127768048952704457311156481550648638322505777201579412750737 (pp66) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.19 hours. Scaled time: 2.78 units (timescale=1.270). Factorization parameters were as follows: n: 34473997445402733752180794441478216709139205993978969681670845367942169957821117137970678303321865177 m: 1000000000000000000000000 c5: 9 c0: 1 skew: 0.6443940149772542505082929811 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64013, largePrimes:2116235 encountered Relations: rels:2216077, finalFF:252753 Max relations in full relation-set: 32 Initial matrix: 113175 x 252753 with sparse part having weight 22900072. Pruned matrix : 83496 x 84125 with weight 4936282. Total sieving time: 1.99 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.19 hours. --------- CPU info (if available) ----------

9·10¹¹³+1 = 9(0)₁₁₂1_<114> = 22699 · 1184459 · C104
C104 = P45 · P60
P45 = 184673635431641860805463910676143935673766213_<45>
P60 = 181263705428764681773841097459967268253297158583781910475797_<60>

Number: 9.113.+1 N=33474627453340210450558941161791675296296994782280919086160013356355525225661891419848286880377772846761 ( 104 digits) SNFS difficulty: 115 digits. Divisors found: r1=184673635431641860805463910676143935673766213 (pp45) r2=181263705428764681773841097459967268253297158583781910475797 (pp60) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.33 hours. Scaled time: 2.97 units (timescale=1.277). Factorization parameters were as follows: n: 33474627453340210450558941161791675296296994782280919086160013356355525225661891419848286880377772846761 m: 100000000000000000000000 c5: 9 c0: 100 skew: 1.618644582767346099223495031 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63918, largePrimes:2311851 encountered Relations: rels:2665234, finalFF:483823 Max relations in full relation-set: 32 Initial matrix: 113080 x 483823 with sparse part having weight 41507232. Pruned matrix : 65593 x 66222 with weight 6026429. Total sieving time: 2.12 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.05 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.33 hours. --------- CPU info (if available) ----------

Apr 5, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
9·10¹¹¹+1 = 9(0)₁₁₀1_<112> = 89 · C111
C111 = P38 · P73
P38 = 76439746214259187150670786361768507023_<38>
P73 = 1322919037723783381478589398425519069856963653988055358561452629090981383_<73>

Number: n N=101123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550561797752809 ( 111 digits) SNFS difficulty: 113 digits. Divisors found: r1=76439746214259187150670786361768507023 (pp38) r2=1322919037723783381478589398425519069856963653988055358561452629090981383 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.17 hours. Scaled time: 1.55 units (timescale=1.324). Factorization parameters were as follows: name: KA_9_0_110_1 n: 101123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550561797752809 skew: 1.22 deg: 5 c5: 10 c0: 27 m: 30000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:114155, AFBsize:114062, largePrimes:4028981 encountered Relations: rels:3581766, finalFF:312084 Max relations in full relation-set: 48 Initial matrix: 228284 x 312084 with sparse part having weight 9536524. Pruned matrix : 136996 x 138201 with weight 2950017. Total sieving time: 0.98 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000 total time: 1.17 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

9·10¹¹⁶+1 = 9(0)₁₁₅1_<117> = 3917 · 719189 · C108
C108 = P34 · P75
P34 = 1814814873154884385579882421783353_<34>
P75 = 176040896601909387016192468843434263374254628094985647651842242628087932409_<75>

Number: n N=319481637436666301862417530975811618189214620608706212631721564718698248156838639004348142600655848305387377 ( 108 digits) SNFS difficulty: 118 digits. Divisors found: r1=1814814873154884385579882421783353 (pp34) r2=176040896601909387016192468843434263374254628094985647651842242628087932409 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.15 hours. Scaled time: 3.12 units (timescale=1.451). Factorization parameters were as follows: name: KA_9_0_115_1 n: 319481637436666301862417530975811618189214620608706212631721564718698248156838639004348142600655848305387377 skew: 1.22 deg: 5 c5: 10 c0: 27 m: 300000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [500000, 600001) Primes: RFBsize:148933, AFBsize:148730, largePrimes:6414980 encountered Relations: rels:5825796, finalFF:426956 Max relations in full relation-set: 28 Initial matrix: 297730 x 426956 with sparse part having weight 22437789. Pruned matrix : 181983 x 183535 with weight 7617386. Total sieving time: 1.61 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.41 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,50000 total time: 2.15 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Apr 5, 2007 (2nd)

By Thomas Womack / ggnfs
(52·10¹⁸⁰-7)/9 = 5(7)_180<181> = 1907145664709063958354268537876114943171_<40> · C142
C142 = P49 · P94
P49 = 2282249079063136761889376337454791894323802478621_<49>
P94 = 1327437030532454031084789475205826920108788207304808616927065055833914814194080582426819377847_<94>

57777_180 factors as 1907145664709063958354268537876114943171 * 2282249079063136761889376337454791894323802478621 * 1327437030532454031084789475205826920108788207304808616927065055833914814194080582426819377847 The calculation took about 300 CPU-hours on a Core2 system, using ggnfs with a factor base bound of 7400000 on each side and a large- prime bound of 2^27; 7883395 relations were collected and converted into 1146658 full relations, which were pruned to a 951774*956854 matrix of sparse-weight 53453875 which took 6.7 hours to solve. The factors were found using the first three dependencies, each sqrt took about nine minutes.

Apr 5, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
9·10¹¹⁷+1 = 9(0)₁₁₆1_<118> = 12527 · C114
C114 = P38 · P77
P38 = 12134790579207611427656536951386453899_<38>
P77 = 59205649022301612078526981553969233951090001376598142943906491679184248013837_<77>

Number: 90001_117 N=718448151991697932465873712780394348207870998642931268460126127564460764748144008940688113674463159575317314600463 ( 114 digits) SNFS difficulty: 117 digits. Divisors found: r1=12134790579207611427656536951386453899 (pp38) r2=59205649022301612078526981553969233951090001376598142943906491679184248013837 (pp77) Version: GGNFS-0.77.1-20050930-k8 Total time: 1.19 hours. Scaled time: 1.08 units (timescale=0.903). Factorization parameters were as follows: n: 718448151991697932465873712780394348207870998642931268460126127564460764748144008940688113674463159575317314600463 m: 100000000000000000000000000000 c4: 90 c0: 1 skew: 1 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 525001) Primes: RFBsize:56543, AFBsize:56607, largePrimes:1944145 encountered Relations: rels:1962930, finalFF:194575 Max relations in full relation-set: 28 Initial matrix: 113217 x 194575 with sparse part having weight 14642351. Pruned matrix : 89791 x 90421 with weight 4553687. Total sieving time: 1.13 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,117,4,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,25000 total time: 1.19 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 4, 2007 (8th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(19·10¹⁵⁵-1)/9 = 2(1)_155<156> = 47 · 1013 · 9323 · C147
C147 = P50 · P97
P50 = 77169526100999077209508970939525278156116721502063_<50>
P97 = 6163143371863327704942361909436417682834706242621502254644653631482204422647185993572154300515649_<97>

Number: n N=475606853299206529041167619811211929776266623611930728781991072004773154333717744575067588796563610919593618264888389363516617868790235646717283887 ( 147 digits) SNFS difficulty: 156 digits. Divisors found: r1=77169526100999077209508970939525278156116721502063 (pp50) r2=6163143371863327704942361909436417682834706242621502254644653631482204422647185993572154300515649 (pp97) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.43 hours. Scaled time: 25.17 units (timescale=0.827). Factorization parameters were as follows: name: KA_2_1_155 n: 475606853299206529041167619811211929776266623611930728781991072004773154333717744575067588796563610919593618264888389363516617868790235646717283887 skew: 1 deg: 5 c5: 19 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216156, largePrimes:6663371 encountered Relations: rels:6163538, finalFF:514891 Max relations in full relation-set: 48 Initial matrix: 433037 x 514891 with sparse part having weight 31257635. Pruned matrix : 360736 x 362965 with weight 16947413. Total sieving time: 26.40 hours. Total relation processing time: 0.32 hours. Matrix solve time: 3.49 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 30.43 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

9·10¹⁵⁵-1 = 8(9)_155<156> = 20201 · 1225603 · C146
C146 = P69 · P77
P69 = 884030473598129112046273401306743817009226878392237244963203638811597_<69>
P77 = 41119951100362876196136581974904931337399314543041289673940222500296800769089_<77>

Number: n N=36351289845585703754357293351820365559093981716913508546008889472133037852153863056158211461589371839905909794802634372142747091837105359572325133 ( 146 digits) SNFS difficulty: 155 digits. Divisors found: r1=884030473598129112046273401306743817009226878392237244963203638811597 (pp69) r2=41119951100362876196136581974904931337399314543041289673940222500296800769089 (pp77) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.22 hours. Scaled time: 29.07 units (timescale=1.030). Factorization parameters were as follows: name: KA_8_9_155 n: 36351289845585703754357293351820365559093981716913508546008889472133037852153863056158211461589371839905909794802634372142747091837105359572325133 type: snfs skew: .68 deg: 5 c5: 9 c0: -1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216846, largePrimes:6333419 encountered Relations: rels:5866544, finalFF:544993 Max relations in full relation-set: 48 Initial matrix: 433726 x 544993 with sparse part having weight 28008672. Pruned matrix : 331320 x 333552 with weight 13763173. Total sieving time: 26.29 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.64 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 28.22 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 3000+ stepping 00 Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem) Calibrating delay loop... 4292.60 BogoMIPS x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 10 Stepping: 0 CPU Model : Athlon XP (Barton) 2.2Ghz processor (estimate).

(28·10¹⁵⁵-1)/9 = 3(1)_155<156> = 281 · 503771 · C148
C148 = P37 · P39 · P73
P37 = 1832323937877638424687563602099971871_<37>
P39 = 528132257091941690986148848873348959257_<39>
P73 = 2271072974612884347124933126129315615770172419175193664363341850801604363_<73>

Number: n N=2197738613463458673765104938773203892054743135182716091261846294825289666128882382672101325759210236475583788427898222997958020616419230301091312461 ( 148 digits) SNFS difficulty: 156 digits. Divisors found: r1=1832323937877638424687563602099971871 (pp37) r2=528132257091941690986148848873348959257 (pp39) r3=2271072974612884347124933126129315615770172419175193664363341850801604363 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.07 hours. Scaled time: 38.39 units (timescale=1.197). Factorization parameters were as follows: name: KA_3_1_155 n: 2197738613463458673765104938773203892054743135182716091261846294825289666128882382672101325759210236475583788427898222997958020616419230301091312461 type: snfs skew: 1 deg: 5 c5: 28 c0: -1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216531, largePrimes:6407029 encountered Relations: rels:5912080, finalFF:529027 Max relations in full relation-set: 28 Initial matrix: 433413 x 529027 with sparse part having weight 28005595. Pruned matrix : 346817 x 349048 with weight 14991508. Total sieving time: 29.48 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.24 hours. Total square root time: 0.15 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 32.07 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 4, 2007 (7th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
9·10¹¹⁴+1 = 9(0)₁₁₃1_<115> = 17 · C114
C114 = P37 · P78
P37 = 4029232093952705808639019244540988181_<37>
P78 = 131392720091863853149542807291473246596308272142652439543027874153558812956013_<78>

Number: 90001_114 N=529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353 ( 114 digits) SNFS difficulty: 114 digits. Divisors found: r1=4029232093952705808639019244540988181 (pp37) r2=131392720091863853149542807291473246596308272142652439543027874153558812956013 (pp78) Version: GGNFS-0.77.1-20050930-k8 Total time: 1.42 hours. Scaled time: 1.20 units (timescale=0.845). Factorization parameters were as follows: n: 529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353 m: 10000000000000000000000000000 c4: 900 c0: 1 skew: 1 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 550001) Primes: RFBsize:37706, AFBsize:41295, largePrimes:1090214 encountered Relations: rels:1015192, finalFF:91472 Max relations in full relation-set: 28 Initial matrix: 79070 x 91472 with sparse part having weight 5609598. Pruned matrix : 76378 x 76837 with weight 3831971. Total sieving time: 1.38 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,114,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,25000 total time: 1.42 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 4, 2007 (6th)

By suberi / GMP-ECM 6.1.2, Msieve 1.16
(16·10²³²-61)/9 = 1(7)₂₃₁1_<233> = 13² · 107 · 5424611 · 2251879303_<10> · 3383480632586611_<16> · 659860332420269216293_<21> · C176
C176 = P33 · C143
P33 = 401303020798046802054496312007947_<33>
C143 = [89826636072279131116714353972287582321596844330753481523328414047161154003015891965880718193219424721650631512860323732891810346797182170707969_<143>]
(16·10²¹³-61)/9 = 1(7)₂₁₂1_<214> = 7 · 11 · 36739 · 701735753995253_<15> · 9242562959716967_<16> · C176 = P38 · C139
P38 = 15343317696192422017522869439279665157_<38>
C139 = [6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851_<139>]
(4·10¹⁹⁹-1)/3 = 1(3)_199<200> = 13 · 55845151 · 75263849 · 2539115591_<10> · 420639307341993281_<18> · 1360635813347265266561_<22> · C135
C135 = P37 · P44 · P56
P37 = 1123948400800834624403052798992224711_<37>
P44 = 12880349982971406781750299797656170118282799_<44>
P56 = 11598857935350921114383370001898924491763276297022728801_<56>

Tue Mar 27 13:24:17 2007 Tue Mar 27 13:24:17 2007 Tue Mar 27 13:24:17 2007 Msieve v. 1.16 Tue Mar 27 13:24:17 2007 random seeds: ff62f22c 6ed97300 Tue Mar 27 13:24:17 2007 factoring 149397349610085003198289424892102693516048525125417141999554174989126877688006523176555899200193999 (99 digits) Tue Mar 27 13:24:18 2007 using multiplier of 1 Tue Mar 27 13:24:18 2007 sieve interval: 9 blocks of size 65536 Tue Mar 27 13:24:18 2007 processing polynomials in batches of 6 Tue Mar 27 13:24:18 2007 using a sieve bound of 2577427 (93822 primes) Tue Mar 27 13:24:18 2007 using large prime bound of 386614050 (28 bits) Tue Mar 27 13:24:18 2007 using double large prime bound of 2864835627027300 (43-52 bits) Tue Mar 27 13:24:18 2007 using trial factoring cutoff of 56 bits Tue Mar 27 13:24:18 2007 polynomial 'A' values have 13 factors Tue Mar 27 22:30:35 2007 Tue Mar 27 22:30:35 2007 Tue Mar 27 22:30:35 2007 Msieve v. 1.16 Tue Mar 27 22:30:35 2007 random seeds: 9434b414 a2be0c24 Tue Mar 27 22:30:35 2007 factoring 149397349610085003198289424892102693516048525125417141999554174989126877688006523176555899200193999 (99 digits) Tue Mar 27 22:30:35 2007 using multiplier of 1 Tue Mar 27 22:30:35 2007 sieve interval: 9 blocks of size 65536 Tue Mar 27 22:30:35 2007 processing polynomials in batches of 6 Tue Mar 27 22:30:35 2007 using a sieve bound of 2577427 (93822 primes) Tue Mar 27 22:30:35 2007 using large prime bound of 386614050 (28 bits) Tue Mar 27 22:30:35 2007 using double large prime bound of 2864835627027300 (43-52 bits) Tue Mar 27 22:30:35 2007 using trial factoring cutoff of 56 bits Tue Mar 27 22:30:35 2007 polynomial 'A' values have 13 factors Tue Mar 27 22:30:48 2007 restarting with 23343 full and 1384965 partial relations Tue Mar 27 22:31:53 2007 94284 relations (23387 full + 70897 combined from 1387390 partial), need 93918 Tue Mar 27 22:31:56 2007 begin with 1410777 relations Tue Mar 27 22:31:58 2007 reduce to 244426 relations in 10 passes Tue Mar 27 22:31:58 2007 attempting to read 244426 relations Tue Mar 27 22:32:03 2007 recovered 244426 relations Tue Mar 27 22:32:03 2007 recovered 231965 polynomials Tue Mar 27 22:32:04 2007 attempting to build 94284 cycles Tue Mar 27 22:32:04 2007 found 94284 cycles in 6 passes Tue Mar 27 22:32:04 2007 distribution of cycle lengths: Tue Mar 27 22:32:04 2007 length 1 : 23387 Tue Mar 27 22:32:04 2007 length 2 : 16540 Tue Mar 27 22:32:04 2007 length 3 : 15894 Tue Mar 27 22:32:04 2007 length 4 : 12715 Tue Mar 27 22:32:04 2007 length 5 : 9498 Tue Mar 27 22:32:04 2007 length 6 : 6539 Tue Mar 27 22:32:04 2007 length 7 : 4103 Tue Mar 27 22:32:04 2007 length 9+: 5608 Tue Mar 27 22:32:04 2007 largest cycle: 19 relations Tue Mar 27 22:32:04 2007 matrix is 93822 x 94284 with weight 6322109 (avg 67.05/col) Tue Mar 27 22:32:05 2007 filtering completed in 4 passes Tue Mar 27 22:32:05 2007 matrix is 92216 x 92280 with weight 6091770 (avg 66.01/col) Tue Mar 27 22:32:06 2007 saving the first 48 matrix rows for later Tue Mar 27 22:32:06 2007 matrix is 92168 x 92280 with weight 4799651 (avg 52.01/col) Tue Mar 27 22:32:06 2007 matrix includes 32 packed rows Tue Mar 27 22:38:17 2007 lanczos halted after 1459 iterations Tue Mar 27 22:38:18 2007 recovered 16 nontrivial dependencies Tue Mar 27 22:38:21 2007 prp44 factor: 12880349982971406781750299797656170118282799 Tue Mar 27 22:38:21 2007 prp56 factor: 11598857935350921114383370001898924491763276297022728801 Tue Mar 27 22:38:21 2007 elapsed time 00:07:46

Apr 4, 2007 (5th)

By Jo Yeong Uk / Msieve 1.17
9·10¹⁷⁷+1 = 9(0)₁₇₆1_<178> = 3167 · 387077 · 2076611 · 308752979 · 54988062023_<11> · 212417999009_<12> · 60289087720622533_<17> · 479166086119340027893509641_<27> · C89
C89 = P32 · P57
P32 = 54841284613190781418275599643521_<32>
P57 = 618783381714794412883445208544663378606596249013437821041_<57>

Wed Apr 4 18:38:40 2007 Wed Apr 4 18:38:40 2007 Wed Apr 4 18:38:40 2007 Msieve v. 1.17 Wed Apr 4 18:38:40 2007 random seeds: 4ee254d4 6fb50e17 Wed Apr 4 18:38:40 2007 factoring 33934875550533712760892172906874721223936456836224646032179227094613311427555598593125361 (89 digits) Wed Apr 4 18:38:40 2007 commencing quadratic sieve (89-digit input) Wed Apr 4 18:38:40 2007 using multiplier of 1 Wed Apr 4 18:38:40 2007 sieve interval: 8 blocks of size 65536 Wed Apr 4 18:38:40 2007 processing polynomials in batches of 7 Wed Apr 4 18:38:40 2007 using a sieve bound of 1556179 (58760 primes) Wed Apr 4 18:38:40 2007 using large prime bound of 124494320 (26 bits) Wed Apr 4 18:38:40 2007 using double large prime bound of 372622455260160 (42-49 bits) Wed Apr 4 18:38:40 2007 using trial factoring cutoff of 49 bits Wed Apr 4 18:38:40 2007 polynomial 'A' values have 11 factors Wed Apr 4 19:42:36 2007 59084 relations (16766 full + 42318 combined from 610550 partial), need 58856 Wed Apr 4 19:42:36 2007 begin with 627316 relations Wed Apr 4 19:42:36 2007 reduce to 139149 relations in 10 passes Wed Apr 4 19:42:36 2007 attempting to read 139149 relations Wed Apr 4 19:42:37 2007 recovered 139149 relations Wed Apr 4 19:42:37 2007 recovered 117719 polynomials Wed Apr 4 19:42:38 2007 attempting to build 59084 cycles Wed Apr 4 19:42:38 2007 found 59084 cycles in 5 passes Wed Apr 4 19:42:38 2007 distribution of cycle lengths: Wed Apr 4 19:42:38 2007 length 1 : 16766 Wed Apr 4 19:42:38 2007 length 2 : 12234 Wed Apr 4 19:42:38 2007 length 3 : 10460 Wed Apr 4 19:42:38 2007 length 4 : 7570 Wed Apr 4 19:42:38 2007 length 5 : 5279 Wed Apr 4 19:42:38 2007 length 6 : 3087 Wed Apr 4 19:42:38 2007 length 7 : 1738 Wed Apr 4 19:42:38 2007 length 9+: 1950 Wed Apr 4 19:42:38 2007 largest cycle: 18 relations Wed Apr 4 19:42:38 2007 matrix is 58760 x 59084 with weight 3361174 (avg 56.89/col) Wed Apr 4 19:42:38 2007 filtering completed in 3 passes Wed Apr 4 19:42:38 2007 matrix is 56982 x 57046 with weight 3171521 (avg 55.60/col) Wed Apr 4 19:42:39 2007 saving the first 48 matrix rows for later Wed Apr 4 19:42:39 2007 matrix is 56934 x 57046 with weight 2578905 (avg 45.21/col) Wed Apr 4 19:42:39 2007 matrix includes 32 packed rows Wed Apr 4 19:43:20 2007 lanczos halted after 902 iterations Wed Apr 4 19:43:20 2007 recovered 14 nontrivial dependencies Wed Apr 4 19:43:20 2007 prp32 factor: 54841284613190781418275599643521 Wed Apr 4 19:43:20 2007 prp57 factor: 618783381714794412883445208544663378606596249013437821041 Wed Apr 4 19:43:20 2007 elapsed time 01:04:40

Apr 4, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(73·10¹⁵⁵-1)/9 = 8(1)_155<156> = 7 · 2381242217_<10> · C146
C146 = P56 · P91
P56 = 15791022294533422641288302975988124695328339669549748081_<56>
P91 = 3081544831696971298063038747475176795596646326721934407174520528715845529258633313218743849_<91>

Number: n N=48660743138931117403363681365899398975704039381650133500834457897155563917113693551241063443598865051121287514059312460533229751601122345218303769 ( 146 digits) SNFS difficulty: 156 digits. Divisors found: r1=15791022294533422641288302975988124695328339669549748081 (pp56) r2=3081544831696971298063038747475176795596646326721934407174520528715845529258633313218743849 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.00 hours. Scaled time: 34.22 units (timescale=1.316). Factorization parameters were as follows: name: KA_8_1_155 n: 48660743138931117403363681365899398975704039381650133500834457897155563917113693551241063443598865051121287514059312460533229751601122345218303769 skew: 1.0 deg: 5 c5: 73 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:217091, largePrimes:6703712 encountered Relations: rels:6172652, finalFF:490474 Max relations in full relation-set: 48 Initial matrix: 433972 x 490474 with sparse part having weight 32278992. Pruned matrix : 383630 x 385863 with weight 19757440. Total sieving time: 22.53 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.22 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 26.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 4, 2007 (3rd)

By Robert Backstrom / GMP-ECM 6.0.1 B1=477500
7·10¹⁵³+1 = 7(0)₁₅₂1_<154> = 53 · 167 · 569 · 173483 · 58181687021_<11> · 240810772871_<12> · 438563879448152243_<18> · C103
C103 = P38 · P65
P38 = 20339748706129911647205888791801144203_<38>
P65 = 64105581640209598722446044764182036063686833229677824048410717867_<65>

Apr 4, 2007 (2nd)

The factor table of 900...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 4, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(29·10¹⁵⁶+7)/9 = 3(2)₁₅₅3_<157> = 47 · C155
C155 = P45 · P111
P45 = 132991322100848707636379191275380420166513791_<45>
P111 = 515506715316065682586052266156769034918158527259325062152327432762009776789896785062695830891823340065597055199_<111>

Number: 32223_156 N=68557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749409 ( 155 digits) SNFS difficulty: 157 digits. Divisors found: r1=132991322100848707636379191275380420166513791 (pp45) r2=515506715316065682586052266156769034918158527259325062152327432762009776789896785062695830891823340065597055199 (pp111) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 55.91 hours. Scaled time: 34.22 units (timescale=0.612). Factorization parameters were as follows: name: 32223_156 n: 68557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749409 m: 10000000000000000000000000000000 c5: 290 c0: 7 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216531, largePrimes:5599595 encountered Relations: rels:5525117, finalFF:486163 Max relations in full relation-set: 0 Initial matrix: 433414 x 486163 with sparse part having weight 34136603. Pruned matrix : 403149 x 405380 with weight 26162517. Total sieving time: 48.51 hours. Total relation processing time: 0.44 hours. Matrix solve time: 6.75 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 55.91 hours. --------- CPU info (if available) ----------

Apr 3, 2007 (9th)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(5·10¹⁸⁸+1)/3 = 1(6)₁₈₇7_<189> = 27749 · C184
C184
C184 = P39 · C145
P39 = 755690361809164985290505633810819050583_<39>
C145 = [7947993980067834235465756271687538769230388089784361354522292128822489146923171127507833276229709407451844578838435579896131515961401437185117001_<145>]

Apr 3, 2007 (8th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
4·10¹⁶²+1 = 4(0)₁₆₁1_<163> = 2497329853_<10> · 75396687085921_<14> · 376268494658838666197_<21> · C119
C119 = P34 · P85
P34 = 7033585355523255976857977544415093_<34>
P85 = 8027072786280128866004929270459039253458495879153981797095597384581952824282996219837_<85>

Apr 3, 2007 (7th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(2·10¹⁵⁵+1)/3 = (6)₁₅₄7_<155> = 1329067 · C149
C149 = P72 · P78
P72 = 288925333565467115077893873169172388791121847831390307889083748917752483_<72>
P78 = 173610601895909678116740701583211225083394536165258694847576929928468819956747_<78>

Number: n N=50160501063277221288818898269738596072783890252836513634501997767356097673530880434670838013935088800389044846246778128316079374980092551140511852801 ( 149 digits) SNFS difficulty: 155 digits. Divisors found: r1=288925333565467115077893873169172388791121847831390307889083748917752483 (pp72) r2=173610601895909678116740701583211225083394536165258694847576929928468819956747 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 27.24 hours. Scaled time: 22.53 units (timescale=0.827). Factorization parameters were as follows: name: KA_6_154_7 n: 50160501063277221288818898269738596072783890252836513634501997767356097673530880434670838013935088800389044846246778128316079374980092551140511852801 skew: 1 deg: 5 c5: 2 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:182816, largePrimes:6581937 encountered Relations: rels:6044442, finalFF:453719 Max relations in full relation-set: 48 Initial matrix: 365953 x 453719 with sparse part having weight 34516891. Pruned matrix : 295057 x 296950 with weight 18465767. Total sieving time: 23.76 hours. Total relation processing time: 0.30 hours. Matrix solve time: 2.98 hours. Total square root time: 0.20 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 27.24 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

(82·10¹⁵⁵-1)/9 = 9(1)_155<156> = 32527021 · C149
C149 = P47 · P103
P47 = 20585795344968187217304961622088033967729763899_<47>
P103 = 1360690654509266104508496867081510258619887149538180594731855032123036171966583286697625777439752406809_<103>

Number: n N=28010899341538566077450225494400827887408167846391807940576885633366520441915388166383607988912083621525349988586754105490051213454534035290569988291 ( 149 digits) SNFS difficulty: 156 digits. Divisors found: r1=20585795344968187217304961622088033967729763899 (pp47) r2=1360690654509266104508496867081510258619887149538180594731855032123036171966583286697625777439752406809 (pp103) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.64 hours. Scaled time: 37.75 units (timescale=1.318). Factorization parameters were as follows: name: KA_9_1_155 n: 28010899341538566077450225494400827887408167846391807940576885633366520441915388166383607988912083621525349988586754105490051213454534035290569988291 skew: 1.0 deg: 5 c5: 82 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216752, largePrimes:7136773 encountered Relations: rels:6741053, finalFF:610738 Max relations in full relation-set: 48 Initial matrix: 433636 x 610738 with sparse part having weight 47311105. Pruned matrix : 290143 x 292375 with weight 22847109. Total sieving time: 25.77 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.60 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

7·10¹⁴⁰+1 = 7(0)₁₃₉1_<141> = 53 · 19597 · 61541309707039_<14> · 52143054355223185883_<20> · C102
C102 = P32 · P71
P32 = 10854524950314912484667997912049_<32>
P71 = 19349001352421860990031887892254003455517463005159744816652778091636397_<71>

Number: n N=210024217943540075133468448585998713651423975051285334416970611675803218930172853494308591985693247453 ( 102 digits) Divisors found: r1=10854524950314912484667997912049 (pp32) r2=19349001352421860990031887892254003455517463005159744816652778091636397 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.73 hours. Scaled time: 7.94 units (timescale=1.027). Factorization parameters were as follows: name: n n: 210024217943540075133468448585998713651423975051285334416970611675803218930172853494308591985693247453 skew: 4857.17 # norm 1.15e+13 c5: 17700 c4: 289407331 c3: -1642729399766 c2: -6867015070714932 c1: 17195621348974928392 c0: 769880280619743055872 # alpha -4.40 Y1: 10035206137 Y0: -25993135675887091241 # Murphy_E 3.01e-09 # M 78178482628374967068165789630605424947992957095981539722006975876156390065512434849895881884496153165 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 Max factor residue bits: 49/49 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:169511, AFBsize:169675, largePrimes:3831878 encountered Relations: rels:3726342, finalFF:397041 Max relations in full relation-set: 48 Initial matrix: 339264 x 397041 with sparse part having weight 19046546. Pruned matrix : 268634 x 270394 with weight 8777420. Total sieving time: 6.72 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.73 hours. Total square root time: 0.11 hours, sqrts: 1. 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: 7.73 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 3000+ stepping 00 Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem) Calibrating delay loop... 4292.60 BogoMIPS x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 10 Stepping: 0 CPU Model : Athlon XP (Barton) 2.2Ghz processor (estimate).

Apr 3, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
3·10¹⁶³+1 = 3(0)₁₆₂1_<164> = C164
C164 = P43 · P122
P43 = 2693727049321118094591486398079193352608837_<43>
P122 = 11136985838101413491867306813366781640721780664180020279181015243224647866545476655493916704578164265918304339860447237773_<122>

Number: 30001_163 N=30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ( 164 digits) SNFS difficulty: 164 digits. Divisors found: r1=2693727049321118094591486398079193352608837 (pp43) r2=11136985838101413491867306813366781640721780664180020279181015243224647866545476655493916704578164265918304339860447237773 (pp122) Version: GGNFS-0.77.1-20050930-k8 Total time: 69.52 hours. Scaled time: 62.78 units (timescale=0.903). Factorization parameters were as follows: n: 30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 m: 500000000000000000000000000000000 c5: 24 c0: 25 skew: 1.01 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5400001) Primes: RFBsize:348513, AFBsize:348511, largePrimes:5904444 encountered Relations: rels:6083619, finalFF:819600 Max relations in full relation-set: 28 Initial matrix: 697090 x 819600 with sparse part having weight 50328626. Pruned matrix : 598977 x 602526 with weight 35613761. Total sieving time: 66.39 hours. Total relation processing time: 0.13 hours. Matrix solve time: 2.94 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.3,2.3,100000 total time: 69.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

7·10¹³³+1 = 7(0)₁₃₂1_<134> = 43 · 31938787737893_<14> · C119
C119 = P34 · P86
P34 = 2453625078680201566748816367059723_<34>
P86 = 20773178568202312946561506523760891062078565941949791090519972188145838947872363815413_<86>

Number: 70001_133 N=50969591898843277031731533454957690483593397704702865881216299727962991255065213977531205848685177328201602448718910599 ( 119 digits) SNFS difficulty: 135 digits. Divisors found: r1=2453625078680201566748816367059723 (pp34) r2=20773178568202312946561506523760891062078565941949791090519972188145838947872363815413 (pp86) Version: GGNFS-0.77.1-20050930-k8 Total time: 5.53 hours. Scaled time: 5.00 units (timescale=0.904). Factorization parameters were as follows: n: 50969591898843277031731533454957690483593397704702865881216299727962991255065213977531205848685177328201602448718910599 m: 500000000000000000000000000 c5: 56 c0: 25 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [650000, 1450001) Primes: RFBsize:100021, AFBsize:100763, largePrimes:1591563 encountered Relations: rels:1628120, finalFF:233486 Max relations in full relation-set: 28 Initial matrix: 200851 x 233486 with sparse part having weight 10220243. Pruned matrix : 184070 x 185138 with weight 6892410. Total sieving time: 5.38 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000 total time: 5.53 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 3, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
4·10¹⁵⁵+1 = 4(0)₁₅₄1_<156> = 7 · 19 · 90173 · C149
C149 = P68 · P81
P68 = 63329687397592132145980877526417873030946686466430656344663544587463_<68>
P81 = 526652909060236900579923203193911048657743442112564846958614597680814721066334503_<81>

Number: n N=33352764097817320073719614485405622558942463897092047542030527951742552682150075931736564193356312831917327836575458252386869717182735375250698135889 ( 149 digits) SNFS difficulty: 155 digits. Divisors found: r1=63329687397592132145980877526417873030946686466430656344663544587463 (pp68) r2=526652909060236900579923203193911048657743442112564846958614597680814721066334503 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.81 hours. Scaled time: 30.85 units (timescale=1.195). Factorization parameters were as follows: name: KA_4_0_154_1 n: 33352764097817320073719614485405622558942463897092047542030527951742552682150075931736564193356312831917327836575458252386869717182735375250698135889 type: snfs skew: 1 deg: 5 c5: 4 c0: 1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:216491, largePrimes:6134762 encountered Relations: rels:5639317, finalFF:512645 Max relations in full relation-set: 28 Initial matrix: 433371 x 512645 with sparse part having weight 23754018. Pruned matrix : 355721 x 357951 with weight 13043634. Total sieving time: 23.48 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.02 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 25.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Apr 3, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
7·10¹⁴⁴+1 = 7(0)₁₄₃1_<145> = 23 · C144
C144 = P66 · P78
P66 = 809940785427965343526229739355042505157936405047381591533420897433_<66>
P78 = 375765527014597615163944861799356289186159071363960150031523628164542872741439_<78>

Number: 70001_144 N=304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826087 ( 144 digits) SNFS difficulty: 145 digits. Divisors found: r1=809940785427965343526229739355042505157936405047381591533420897433 (pp66) r2=375765527014597615163944861799356289186159071363960150031523628164542872741439 (pp78) Version: GGNFS-0.77.1-20050930-k8 Total time: 14.94 hours. Scaled time: 13.49 units (timescale=0.903). Factorization parameters were as follows: n: 304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826087 m: 100000000000000000000000000000 c5: 7 c0: 10 skew: 1.07 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1600001) Primes: RFBsize:114155, AFBsize:114342, largePrimes:2746135 encountered Relations: rels:2738222, finalFF:297904 Max relations in full relation-set: 28 Initial matrix: 228562 x 297904 with sparse part having weight 23793466. Pruned matrix : 205655 x 206861 with weight 13817480. Total sieving time: 14.65 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.21 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 14.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 3, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
7·10¹⁵⁵+1 = 7(0)₁₅₄1_<156> = 1129 · 1193 · C150
C150 = P62 · P88
P62 = 55130793260966415361235729756577932205405829083406166227977587_<62>
P88 = 9426911131444313172543736731542159160773688947699429609478209619825750212976152411926859_<88>

Number: n N=519713088677159426444635335886856975700443315264641616990757273941511489000272478147920739299293115954672109300117232423860176390622297027909335309233 ( 150 digits) SNFS difficulty: 155 digits. Divisors found: r1=55130793260966415361235729756577932205405829083406166227977587 (pp62) r2=9426911131444313172543736731542159160773688947699429609478209619825750212976152411926859 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 27.19 hours. Scaled time: 27.90 units (timescale=1.026). Factorization parameters were as follows: name: KA_7_0_154_1 n: 519713088677159426444635335886856975700443315264641616990757273941511489000272478147920739299293115954672109300117232423860176390622297027909335309233 type: snfs skew: .68 deg: 5 c5: 7 c0: 1 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:216696, largePrimes:6092352 encountered Relations: rels:5565111, finalFF:487372 Max relations in full relation-set: 48 Initial matrix: 433579 x 487372 with sparse part having weight 24045932. Pruned matrix : 379538 x 381769 with weight 14885224. Total sieving time: 24.79 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.03 hours. Total square root time: 0.15 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 27.19 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 3000+ stepping 00 Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem) Calibrating delay loop... 4292.60 BogoMIPS x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 10 Stepping: 0 CPU Model : Athlon XP (Barton) 2.2Ghz processor (estimate).

Apr 3, 2007 (2nd)

By Alfred Reich / GMP-ECM B1=250000
10¹⁷⁹²+1 = 1(0)₁₇₉₁1_<1793> = 10753 · 32257 · 8253953 · 9524994049_<10> · 73171503617_<11> · 45723922339769773677559297_<26> · 161659663356434944948942201164163009493717089102370771373121362150985544514761379133487997023996012149425048654486737380370333511296921220558813648612791137845552210697266256120930676972710885926127946416909582894897995807233_<225> · C1506
C1506 = P30 · C1476
P30 = 949383321082513089661541033473_<30>

Apr 3, 2007

By Bruce Dodson / GMP-ECM B1=43000000 / Mar 30, 2007
10³⁶¹+1 = 1(0)₃₆₀1_<362> = 11 · 43321 · 909090909090909091_<18> · C338
C338 = P55 · C283
P55 = 5140192330491733331414521378576126342075768810496980939_<55>
By Yousuke Koide / GMP-ECM B1=1250000 / Apr 2, 2007
(10⁸⁹⁵-1)/9 = (1)_895<895> = 41 · 271 · 359 · 36558961 · 252812074841_<12> · 4201521652717_<13> · 352543640588653_<15> · 571544047837540227171107263031017853607119654486278118381637405539602949994236278780111557713711574640626700398384915989416568503505447054089_<141> · C701
C701 = P42 · C660
P42 = 160448729579634932307271265568632037109271_<42>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 2, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
7·10¹³⁸+1 = 7(0)₁₃₇1_<139> = 683 · 323565643 · C128
C128 = P34 · P94
P34 = 5455759339741710826253913205440113_<34>
P94 = 5805768712228287085116276448327387554343755401317995474938232335903884659779580329249392645433_<94>

Number: 70001_138 N=31674876876119682273182173592100422640303476152979377067510779551529709019971793502322392463306558652053674526010259588124453929 ( 128 digits) SNFS difficulty: 140 digits. Divisors found: r1=5455759339741710826253913205440113 (pp34) r2=5805768712228287085116276448327387554343755401317995474938232335903884659779580329249392645433 (pp94) Version: GGNFS-0.77.1-20050930-k8 Total time: 10.45 hours. Scaled time: 9.26 units (timescale=0.886). Factorization parameters were as follows: n: 31674876876119682273182173592100422640303476152979377067510779551529709019971793502322392463306558652053674526010259588124453929 m: 5000000000000000000000000000 c5: 56 c0: 25 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [650000, 1250001) Primes: RFBsize:100021, AFBsize:100763, largePrimes:1595353 encountered Relations: rels:1636224, finalFF:234205 Max relations in full relation-set: 28 Initial matrix: 200851 x 234205 with sparse part having weight 10228624. Pruned matrix : 183788 x 184856 with weight 6854937. Total sieving time: 10.30 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000 total time: 10.45 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 2, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=3000000
(16·10¹⁸⁷-61)/9 = 1(7)₁₈₆1_<188> = 11 · C187
C187 = P36 · P151
P36 = 224187443841669121284171214256607419_<36>
P151 = 7208974724307126960936798016662298358054035706538253992990330169438604402959170146020867892824891898686186801010965926966443527148977721432936345060819_<151>

Apr 2, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(2·10¹⁵⁵+43)/9 = (2)₁₅₄7_<155> = 3² · 31 · C152
C152 = P42 · P50 · P61
P42 = 661935245772807400405303706022642863715601_<42>
P50 = 39969992495755205306998842332734817740510356056777_<50>
P61 = 3010465883270152612607869483290283204139039754469978537289069_<61>

Number: n N=79649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133413 ( 152 digits) SNFS difficulty: 155 digits. Divisors found: r1=661935245772807400405303706022642863715601 (pp42) r2=39969992495755205306998842332734817740510356056777 (pp50) r3=3010465883270152612607869483290283204139039754469978537289069 (pp61) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.67 hours. Scaled time: 25.36 units (timescale=0.827). Factorization parameters were as follows: name: KA_2_154_7 n: 79649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133413 skew: 1 deg: 5 c5: 2 c0: 43 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:183072, AFBsize:183126, largePrimes:6529615 encountered Relations: rels:5939827, finalFF:413909 Max relations in full relation-set: 48 Initial matrix: 366263 x 413909 with sparse part having weight 31561080. Pruned matrix : 329480 x 331375 with weight 20050356. Total sieving time: 26.37 hours. Total relation processing time: 0.31 hours. Matrix solve time: 3.66 hours. Total square root time: 0.33 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 30.67 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS

7·10¹³²+1 = 7(0)₁₃₁1_<133> = 3917 · 8731 · C126
C126 = P47 · P80
P47 = 14638283495713663736241157708855869290229636409_<47>
P80 = 13982677029538623333501754987296211103374639783010627959614701454655065820539607_<80>

Number: n N=204682390387389786939374567224670824662719240059899424336625103763006798350154668248296231092500738391723322508656383793751263 ( 126 digits) SNFS difficulty: 132 digits. Divisors found: r1=14638283495713663736241157708855869290229636409 (pp47) r2=13982677029538623333501754987296211103374639783010627959614701454655065820539607 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.29 hours. Scaled time: 6.32 units (timescale=1.195). Factorization parameters were as follows: name: KA_7_0_131_1 n: 204682390387389786939374567224670824662719240059899424336625103763006798350154668248296231092500738391723322508656383793751263 type: snfs skew: .27 deg: 5 c5: 700 c0: 1 m: 100000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:148933, AFBsize:148445, largePrimes:5256226 encountered Relations: rels:4734818, finalFF:475275 Max relations in full relation-set: 28 Initial matrix: 297445 x 475275 with sparse part having weight 14694290. Pruned matrix : 149989 x 151540 with weight 4433861. Total sieving time: 4.88 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.24 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.2,2.2,50000 total time: 5.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(32·10¹⁵⁵-23)/9 = 3(5)₁₅₄3_<156> = 11 · 6121 · C151
C151 = P44 · P107
P44 = 61328780631367967021026430277387968633477083_<44>
P107 = 86104941161045057261632331707436338464311272986903568019467121044209094189256912159281648305922546899162961_<107>

Number: n N=5280711047742578538200168652709087278602063767886345896474960353411586870172068669046287082555666120443117665793699121586721652070451286265695675922763 ( 151 digits) SNFS difficulty: 156 digits. Divisors found: r1=61328780631367967021026430277387968633477083 (pp44) r2=86104941161045057261632331707436338464311272986903568019467121044209094189256912159281648305922546899162961 (pp107) Version: GGNFS-0.77.1-20051202-athlon Total time: 20.77 hours. Scaled time: 27.49 units (timescale=1.324). Factorization parameters were as follows: name: KA_3_5_154_3 n: 5280711047742578538200168652709087278602063767886345896474960353411586870172068669046287082555666120443117665793699121586721652070451286265695675922763 skew: 1.0 deg: 5 c5: 1 c0: -23 m: 20000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:183106, largePrimes:6476865 encountered Relations: rels:5900796, finalFF:422371 Max relations in full relation-set: 48 Initial matrix: 366242 x 422371 with sparse part having weight 31319894. Pruned matrix : 321698 x 323593 with weight 18573106. Total sieving time: 18.14 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.41 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 20.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 2, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=1500000
(16·10²⁴³-61)/9 = 1(7)₂₄₂1_<244> = 7 · 11 · 30296731 · 60143609 · 1911168697_<10> · C217
C217 = P32 · P185
P32 = 73816070285390658060425630041457_<32>
P185 = 89815552858504538029397848590765921832955963914835824465961063265706776182932599671826275231815308372814936304804714931802441141565531885161718561173705190056377611445342403457383082453_<185>

Apr 2, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
7·10¹⁴⁵+1 = 7(0)₁₄₄1_<146> = 67 · 599 · 412457 · 466747 · 1141698744217337_<16> · 2434518084465653_<16> · C100
C100 = P34 · P67
P34 = 1795008466954729168800209414936453_<34>
P67 = 1815955371841082430332694563327821684185611841419005671789292422271_<67>

Number: 70001_145 N=3259655268066666531787153780348226028624564585225737486803402609014796394727034639592215715906944763 ( 100 digits) Divisors found: r1=1795008466954729168800209414936453 (pp34) r2=1815955371841082430332694563327821684185611841419005671789292422271 (pp67) Version: GGNFS-0.77.1-20050930-k8 Total time: 4.36 hours. Scaled time: 3.94 units (timescale=0.904). Factorization parameters were as follows: name: 70001_145 n: 3259655268066666531787153780348226028624564585225737486803402609014796394727034639592215715906944763 skew: 5434.66 # norm 8.87e+13 c5: 138600 c4: -628977735 c3: -4844662654778 c2: 56975616878785198 c1: 12597830851657240872 c0: -315955197528020586762632 # alpha -6.43 Y1: 27202766879 Y0: -7486573984825469671 # Murphy_E 3.49e-09 # M 2021588631885662640472603336663148478076687078668088154026142239430095812078564709322760587979382906 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [750000, 1200001) Primes: RFBsize:114155, AFBsize:114915, largePrimes:3762566 encountered Relations: rels:3629001, finalFF:277528 Max relations in full relation-set: 28 Initial matrix: 229154 x 277528 with sparse part having weight 19757876. Pruned matrix : 193470 x 194679 with weight 11201879. Polynomial selection time: 0.25 hours. Total sieving time: 3.82 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.16 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000 total time: 4.36 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 2, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁵+23)/9 = (4)₁₅₄7_<155> = 13 · 61 · C152
C152 = P54 · P99
P54 = 148385991234646868255677763169400682719601527549176821_<54>
P99 = 377703833218830785744902903453732714767953802089122910383042080301772785279239335742045411173229499_<99>

Number: n N=56045957685301947597029564242678996777357433095138013170800056045957685301947597029564242678996777357433095138013170800056045957685301947597029564242679 ( 152 digits) SNFS difficulty: 155 digits. Divisors found: r1=148385991234646868255677763169400682719601527549176821 (pp54) r2=377703833218830785744902903453732714767953802089122910383042080301772785279239335742045411173229499 (pp99) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.59 hours. Scaled time: 36.56 units (timescale=1.195). Factorization parameters were as follows: name: KA_4_154_7 n: 56045957685301947597029564242678996777357433095138013170800056045957685301947597029564242678996777357433095138013170800056045957685301947597029564242679 type: snfs skew: 1 deg: 5 c5: 4 c0: 23 m: 10000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [1600000, 1600000) Primes: RFBsize:230209, AFBsize:230627, largePrimes:6238983 encountered Relations: rels:5736835, finalFF:526134 Max relations in full relation-set: 28 Initial matrix: 460900 x 526134 with sparse part having weight 23788925. Pruned matrix : 395232 x 397600 with weight 14177810. Total sieving time: 27.64 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.50 hours. Total square root time: 0.26 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 30.59 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

7·10¹³¹+1 = 7(0)₁₃₀1_<132> = 16573 · 827182080526619_<15> · C113
C113 = P32 · P81
P32 = 60570823643539584765292420545299_<32>
P81 = 843009197215127294834358695906019746493107625259983272341093175391722476971875477_<81>

Number: n N=51061761414399357027026281791696991073532907727375622679324186881116608610691045434679404986513298702271065732623 ( 113 digits) SNFS difficulty: 131 digits. Divisors found: r1=60570823643539584765292420545299 (pp32) r2=843009197215127294834358695906019746493107625259983272341093175391722476971875477 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.67 hours. Scaled time: 6.85 units (timescale=1.027). Factorization parameters were as follows: name: KA_7_0_130_1 n: 51061761414399357027026281791696991073532907727375622679324186881116608610691045434679404986513298702271065732623 type: snfs skew: 2.34 deg: 5 c5: 70 c0: 1 m: 100000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:148933, AFBsize:149260, largePrimes:4789248 encountered Relations: rels:4160441, finalFF:353209 Max relations in full relation-set: 48 Initial matrix: 298260 x 353209 with sparse part having weight 10465394. Pruned matrix : 209368 x 210923 with weight 4935962. Total sieving time: 6.13 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.34 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.2,2.2,50000 total time: 6.67 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 3000+ stepping 00 Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem) Calibrating delay loop... 4292.60 BogoMIPS x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 10 Stepping: 0 CPU Model : Athlon XP (Barton) 2.2Ghz processor (estimate).

Apr 1, 2007 (7th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs
7·10¹⁵⁷+1 = 7(0)₁₅₆1_<158> = 107 · 131 · 257 · 44701 · 36067159 · 412688953 · 11433124763162139881_<20> · 50150999103831809543_<20> · C92
C92 = P44 · P48
P44 = 58723657563182981121109730736410322969118927_<44>
P48 = 867361611497461809778725449710059255808380370747_<48>

Number: n N=50934646257027501761195466390338358257517450725863747999950593705003914525713753040194828469 ( 92 digits) Divisors found: r1=58723657563182981121109730736410322969118927 (pp44) r2=867361611497461809778725449710059255808380370747 (pp48) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.26 hours. Scaled time: 4.37 units (timescale=1.027). Factorization parameters were as follows: name: KA_7_0_156_1 n: 50934646257027501761195466390338358257517450725863747999950593705003914525713753040194828469 m: 1232264682236136063145 deg: 4 c4: 22090080 c3: -246466740744 c2: -33306940536444256 c1: 1000581673960989041 c0: 43321014325197429213924 skew: 1635.250 type: gnfs # adj. I(F,S) = 53.214 # E(F1,F2) = 1.198140e-04 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1175417502. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 40000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [175000, 655001) Primes: RFBsize:56543, AFBsize:57008, largePrimes:1529129 encountered Relations: rels:1493247, finalFF:136569 Max relations in full relation-set: 48 Initial matrix: 113627 x 136569 with sparse part having weight 12059376. Pruned matrix : 106514 x 107146 with weight 7026392. Polynomial selection time: 0.17 hours. Total sieving time: 3.73 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.17 hours. Total square root time: 0.10 hours, sqrts: 3. Prototype def-par.txt line would be: gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000 total time: 4.26 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 3000+ stepping 00 Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem) Calibrating delay loop... 4292.60 BogoMIPS x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 10 Stepping: 0 CPU Model : Athlon XP (Barton) 2.2Ghz processor (estimate).

Apr 1, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
7·10¹¹⁸+1 = 7(0)₁₁₇1_<119> = 233 · 2053 · 3761 · 68777 · C105
C105 = P45 · P60
P45 = 573478493821804383126117265442725302450908591_<45>
P60 = 986482696674090871440722049772557294942194567424256350401987_<60>

Number: 70001_118 N=565726611069929549103721920736813842762633274721108994347074829384094876815420884707818446157636241770317 ( 105 digits) SNFS difficulty: 120 digits. Divisors found: r1=573478493821804383126117265442725302450908591 (pp45) r2=986482696674090871440722049772557294942194567424256350401987 (pp60) Version: GGNFS-0.77.1-20050930-k8 Total time: 1.23 hours. Scaled time: 1.11 units (timescale=0.908). Factorization parameters were as follows: n: 565726611069929549103721920736813842762633274721108994347074829384094876815420884707818446157636241770317 m: 500000000000000000000000 c5: 56 c0: 25 skew: 1 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 500001) Primes: RFBsize:56543, AFBsize:56853, largePrimes:2008292 encountered Relations: rels:2032184, finalFF:180139 Max relations in full relation-set: 28 Initial matrix: 113463 x 180139 with sparse part having weight 15070540. Pruned matrix : 95115 x 95746 with weight 5531881. Total sieving time: 1.15 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,25000 total time: 1.23 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

7·10¹²⁹+1 = 7(0)₁₂₈1_<130> = C130
C130 = P47 · P84
P47 = 20339094283792370330464042356579607994600801891_<47>
P84 = 344164784445593301152541755553359867327580661913692995263470054136783938426510011211_<84>

Number: 70001_129 N=7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ( 130 digits) SNFS difficulty: 130 digits. Divisors found: r1=20339094283792370330464042356579607994600801891 (pp47) r2=344164784445593301152541755553359867327580661913692995263470054136783938426510011211 (pp84) Version: GGNFS-0.77.1-20050930-k8 Total time: 3.36 hours. Scaled time: 3.05 units (timescale=0.906). Factorization parameters were as follows: n: 7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 m: 100000000000000000000000000 c5: 7 c0: 10 skew: 1.07 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1050001) Primes: RFBsize:78498, AFBsize:78531, largePrimes:1534031 encountered Relations: rels:1534832, finalFF:179547 Max relations in full relation-set: 28 Initial matrix: 157094 x 179547 with sparse part having weight 10290326. Pruned matrix : 149259 x 150108 with weight 7019841. Total sieving time: 3.25 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.07 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 3.36 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239) Total of 2 processors activated (9340.09 BogoMIPS).

Apr 1, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(67·10¹⁵⁵+23)/9 = 7(4)₁₅₄7_<156> = 3² · 11 · 59 · 757 · 1277 · 769297 · 1235879 · 433604364641179_<15> · C120
C120 = P50 · P71
P50 = 22928700027420573259550411439689826644603502508189_<50>
P71 = 13948106057056804745088320535643843511280832362656801314221379280509351_<71>

Number: n N=319811939732903422928211520638581135594400328539761352160261824264315953518741377685581991531923423122342513529968575339 ( 120 digits) SNFS difficulty: 156 digits. Divisors found: r1=22928700027420573259550411439689826644603502508189 (pp50) r2=13948106057056804745088320535643843511280832362656801314221379280509351 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.49 hours. Scaled time: 29.26 units (timescale=1.027). Factorization parameters were as follows: name: KA_7_4_154_7 n: 319811939732903422928211520638581135594400328539761352160261824264315953518741377685581991531923423122342513529968575339 type: snfs skew: 1 deg: 5 c5: 67 c0: 23 m: 10000000000000000000000000000000 rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [700000, 1700001) Primes: RFBsize:203362, AFBsize:203097, largePrimes:6631404 encountered Relations: rels:6131336, finalFF:499186 Max relations in full relation-set: 48 Initial matrix: 406524 x 499186 with sparse part having weight 36598443. Pruned matrix : 333552 x 335648 with weight 20323473. Total sieving time: 25.34 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.56 hours. Total square root time: 0.41 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000 total time: 28.49 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 3000+ stepping 00 Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem) Calibrating delay loop... 4292.60 BogoMIPS x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 10 Stepping: 0 CPU Model : Athlon XP (Barton) 2.2Ghz processor (estimate).

Apr 1, 2007 (4th)

The factor table of 700...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 1, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
3·10¹⁵⁵+1 = 3(0)₁₅₄1_<156> = 13 · 29² · C152
C152 = P42 · P51 · P60
P42 = 847002118930358570602520920381717175156063_<42>
P51 = 213090300524279549137442960054809434214996463074123_<51>
P60 = 152031551632891694465641580404499699339343734544590141354153_<60>

Number: n N=27439860971371078386536174883380590871672916857221256745632488795390103356809658831061922619592060733558949967986828866733741882374462636055977316381597 ( 152 digits) SNFS difficulty: 155 digits. Divisors found: r1=847002118930358570602520920381717175156063 (pp42) r2=213090300524279549137442960054809434214996463074123 (pp51) r3=152031551632891694465641580404499699339343734544590141354153 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.48 hours. Scaled time: 25.79 units (timescale=1.324). Factorization parameters were as follows: name: KA_3_0_154_1 n: 27439860971371078386536174883380590871672916857221256745632488795390103356809658831061922619592060733558949967986828866733741882374462636055977316381597 skew: 1.0 deg: 5 c5: 3 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:183166, largePrimes:6441974 encountered Relations: rels:5875787, finalFF:426749 Max relations in full relation-set: 48 Initial matrix: 366303 x 426749 with sparse part having weight 31449065. Pruned matrix : 316723 x 318618 with weight 18266116. Total sieving time: 16.85 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.29 hours. Total square root time: 0.18 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 19.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Apr 1, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
3·10¹⁷⁸+1 = 3(0)₁₇₇1_<179> = 2050459 · 12264541 · 340688242377207018081711127_<27> · C139
C139 = P31 · P108
P31 = 5069346827014420672241942756293_<31>
P108 = 690732220068543526727568186205626712603241853899400661384995347253624067067728995244495344555464573552973589_<108>
3·10¹⁶²+1 = 3(0)₁₆₁1_<163> = 7130941393003213_<16> · C147
C147 = P36 · C112
P36 = 103809697153908617469853075665675511_<36>
C112 = [4052625413616873991636843572634283505999285953539026570840954837694883840351540445126100833603885531257627444707_<112>]

Apr 1, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(2·10¹⁷²+43)/9 = (2)₁₇₁7_<172> = C172
C172 = P43 · P130
P43 = 1754614804757565785712489120426881346518977_<43>
P130 = 1266501465846952949874835380376498574495553770154845880082310728334619055651692455210844385139552416214859403953453928983218567251_<130>

Number: n N=2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 ( 172 digits) SNFS difficulty: 172 digits. Divisors found: r1=1754614804757565785712489120426881346518977 (pp43) r2=1266501465846952949874835380376498574495553770154845880082310728334619055651692455210844385139552416214859403953453928983218567251 (pp130) Version: GGNFS-0.77.1-20051202-athlon Total time: 271.55 hours. Scaled time: 224.57 units (timescale=0.827). Factorization parameters were as follows: name: KA_C172_2_171_7 n: 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 skew: 1 deg: 5 c5: 200 c0: 43 m: 10000000000000000000000000000000000 type: snfs rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 200000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [2400000, 10000001) Primes: RFBsize:335439, AFBsize:335372, largePrimes:8991273 encountered Relations: rels:8540919, finalFF:760748 Max relations in full relation-set: 48 Initial matrix: 670876 x 760748 with sparse part having weight 107554650. Pruned matrix : 626583 x 630001 with weight 85954256. Total sieving time: 236.73 hours. Total relation processing time: 0.72 hours. Matrix solve time: 33.80 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,48,48,2.5,2.5,100000 total time: 271.55 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2100+ stepping 02 Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem) Calibrating delay loop... 3440.64 BogoMIPS