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News and updates, July 2006

Jul 31, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10¹⁸¹-31)/9 = (4)₁₈₀1_<181> = 691 · C178
C178 = P35 · C144
P35 = 18341311570927686739221204596281603_<35>
C144 = [350678423961842493729246583229724423685615232184993031214145040572519155068819591779849294477911743031232439012498194912517275810305005552598017_<144>]

Jul 30, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(8·10¹⁹⁴+1)/9 = (8)₁₉₃9_<194> = 7129 · 7193 · 490057 · 13676537335459_<14> · 59621355333702961_<17> · C151
C151 = P35 · P117
P35 = 12622486933254640856936731027878923_<35>
P117 = 343668142793819369342868699647116068318546166592509493762943274316967670246952436452566986782105405574673788064694033_<117>

Jul 26, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs
(8·10¹⁸⁴+1)/9 = (8)₁₈₃9_<184> = 3 · 19603 · 172173708801163613627_<21> · C159
C159 = P29 · C131
P29 = 27179099398845119796776615939_<29>
C131 = [32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457_<131>]
(8·10¹⁸¹+1)/9 = (8)₁₈₀9_<181> = 3² · 162703 · 436529 · C170
C170 = P39 · C131
P39 = 198685966079416987465648073668331204609_<39>
C131 = [69988891390170684419064864292472492567266787296607386124102937093503944074615798168449992226257202972265875496995584237861973115887_<131>]
(8·10¹⁷⁵+1)/9 = (8)₁₇₄9_<175> = 3 · 103 · 270950423 · 24229424690721201848947_<23> · C142
C142 = P37 · P43 · P64
P37 = 1187459593948663942345533369324773863_<37>
P43 = 1621372469742717880365943926655152482024861_<43>
P64 = 2275906557941688510267400481774821829901703819890554273677954787_<64>

Number: template N=3690092236753563552546589205826588094126097050469521337750003386324822725505644653827392179184738967959607 ( 106 digits) Divisors found: r1=1621372469742717880365943926655152482024861 (pp43) r2=2275906557941688510267400481774821829901703819890554273677954787 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 13.34 hours. Scaled time: 16.68 units (timescale=1.250). Factorization parameters were as follows: name: template n: 3690092236753563552546589205826588094126097050469521337750003386324822725505644653827392179184738967959607 skew: 17540.76 # norm 2.22e+014 c5: 18540 c4: 445661492 c3: -20154034773225 c2: -117243062043128466 c1: 2055231393406905905146 c0: 6780112294565646891804960 # alpha -5.98 Y1: 90312434587 Y0: -181879797367810544261 # Murphy_E 1.89e-009 # M 559630045337832813518883705861953988295828468353446159222632565406767852774425818137205583461403479764802 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: RFBsize:183072, AFBsize:182547, largePrimes:4443465 encountered Relations: rels:4565926, finalFF:502025 Max relations in full relation-set: 28 Initial matrix: 365702 x 502025 with sparse part having weight 36650530. Pruned matrix : 257832 x 259724 with weight 17722141. Total sieving time: 11.85 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.12 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 13.34 hours. --------- CPU info (if available) ----------

(8·10¹⁸⁷+1)/9 = (8)₁₈₆9_<187> = 3 · 263 · 26821 · 88883 · 1119746363_<10> · 918134378332008821_<18> · C148
C148 = P33 · P36 · P80
P33 = 165805694449843257500642766390827_<33>
P36 = 934070656153121251699814499393013861_<36>
P80 = 29680534863754695395148746244944140636632693438105910924697912984920615447644347_<80>

Jul 23, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁶⁶-7)/9 = 9(7)_166<167> = 107 · 22585789 · 644297617169_<12> · 4056411030394169_<16> · C131
C131 = P60 · P71
P60 = 795997355428448940999990564851890555756567795185419778731011_<60>
P71 = 19448271711557563851095010492190619092216476162100540985170829304296669_<71>

Number: 97777_166 N=15480772850053735174812154400698448628670785732665450293762375478799791273005124409888204255075924043017964918964150912682694302359 ( 131 digits) SNFS difficulty: 168 digits. Divisors found: r1=795997355428448940999990564851890555756567795185419778731011 (pp60) r2=19448271711557563851095010492190619092216476162100540985170829304296669 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 211.66 hours. Scaled time: 142.23 units (timescale=0.672). Factorization parameters were as follows: name: 97777_166 n: 15480772850053735174812154400698448628670785732665450293762375478799791273005124409888204255075924043017964918964150912682694302359 m: 2000000000000000000000000000000000 c5: 55 c0: -14 skew: 2 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 7150001) Primes: RFBsize:380800, AFBsize:380438, largePrimes:6071781 encountered Relations: rels:6279833, finalFF:858677 Max relations in full relation-set: 28 Initial matrix: 761304 x 858677 with sparse part having weight 61581012. Pruned matrix : 685817 x 689687 with weight 47025780. Total sieving time: 181.11 hours. Total relation processing time: 0.93 hours. Matrix solve time: 29.30 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 211.66 hours. --------- CPU info (if available) ----------

Jul 23, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10¹⁹⁰+9 = 1(0)₁₈₉9_<191> = 17 · 661 · 3617 · 9255737 · C176
C176 = P38 · C138
P38 = 58578835214747005278058475891560020601_<38>
C138 = [453784202451725518980480133089420040136273460591104916659256777047754295589507064687162836139574199000297912034696834143699088261379945733_<138>]
10¹⁷¹+9 = 1(0)₁₇₀9_<172> = 114870713498291_<15> · 152103797335211_<15> · C176
C143 = P31 · C113
P31 = 1077903296318851813591058561693_<31>
C113 = [53097102801403831665746807018118510756849451124526459253855124796660194850247112567565191453771626718853971948813_<113>]

Jul 17, 2006

By Alfred Reich / Msieve V 1.06
(10¹⁶¹+71)/9 = (1)₁₆₀9_<161> = 23327 · 321131832988051_<15> · 1191317231086892298689_<22> · C121
C121 = P39 · P82
P39 = 157827640943815926474954927538137344371_<39>
P82 = 7888687536686028472531832671390978588451330433797341725738861291549234482598071113_<82>

Jul 15, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10¹⁶¹-1)/3 = 7(3)_161<162> = 73 · 34653533 · C153
C153 = P32 · C122
P32 = 22935196665910109914667553700279_<32>
C122 = [12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503_<122>]
(25·10¹⁹⁷-1)/3 = 8(3)_197<198> = 656603 · 170454115654360806479399_<24> · C169
C169 = P33 · P137
P33 = 165593497569484456997057320046729_<33>
P137 = 44964018754490646891491038249988341848259629720873308924575013742259137181650315743036690343984815431548345392057804704806670264403772241_<137>
(22·10¹⁵²-1)/3 = 7(3)_152<153> = 417587987 · 10350831019_<11> · C135
C135 = P35 · P100
P35 = 17497935690527231337957237637215421_<35>
P100 = 9695972941720835118569525522840796078591641123474745316988805837411044124787063482971552015328045641_<100>

Jul 14, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁶⁵-7)/9 = 9(7)_165<166> = 3 · C166
C166 = P77 · P89
P77 = 45346200595934146934131296942427106498745059419385026179154277004358396423331_<77>
P89 = 71875024068752797477559446177335736254751869797365522711198282153882911150417196506178889_<89>

Number: 97777_165 N=3259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 ( 166 digits) SNFS difficulty: 166 digits. Divisors found: r1=45346200595934146934131296942427106498745059419385026179154277004358396423331 (pp77) r2=71875024068752797477559446177335736254751869797365522711198282153882911150417196506178889 (pp89) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 178.89 hours. Scaled time: 120.39 units (timescale=0.673). Factorization parameters were as follows: name: 97777_165 n: 3259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 m: 1000000000000000000000000000000000 c5: 88 c0: -7 skew: 2 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, ) Primes: RFBsize:348513, AFBsize:348862, largePrimes:6048552 encountered Relations: rels:6244545, finalFF:823730 Max relations in full relation-set: 28 Initial matrix: 697441 x 823730 with sparse part having weight 63288732. Pruned matrix : 602166 x 605717 with weight 47023567. Total sieving time: 158.14 hours. Total relation processing time: 0.93 hours. Matrix solve time: 19.53 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 178.89 hours. --------- CPU info (if available) ----------

Jul 14, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4
(7·10¹⁵⁴-61)/9 = (7)₁₅₃1_<154> = 59040511 · 30846605261_<11> · C136
C136 = P36 · P41 · P60
P36 = 169750613328204889527307493147334971_<36>
P41 = 70847408418392222124674327036637004102729_<41>
P60 = 355109856140986847622896672372910163920648639023544483933139_<60>

Number: 77771_154 N=4270689989174991981377200663819930402301374317453540384390776208047194568640332560832240274686466139739702588331996549083657274648231401 ( 136 digits) SNFS difficulty: 155 digits. Divisors found: r1=169750613328204889527307493147334971 (pp36) r2=70847408418392222124674327036637004102729 (pp41) r3=355109856140986847622896672372910163920648639023544483933139 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 55.96 hours. Scaled time: 35.92 units (timescale=0.642). Factorization parameters were as follows: n: 4270689989174991981377200663819930402301374317453540384390776208047194568640332560832240274686466139739702588331996549083657274648231401 m: 10000000000000000000000000000000 c5: 7 c0: -610 skew: 2.44 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:217162, largePrimes:5654054 encountered Relations: rels:5570235, finalFF:503190 Max relations in full relation-set: 28 Initial matrix: 434043 x 503190 with sparse part having weight 42264052. Pruned matrix : 404056 x 406290 with weight 30433715. Total sieving time: 46.92 hours. Total relation processing time: 0.38 hours. Matrix solve time: 8.44 hours. Time per square root: 0.22 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: 55.96 hours. --------- CPU info (if available) ----------

Jul 14, 2006

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4
10¹³⁹+9 = 1(0)₁₃₈9_<140> = 23 · 881 · 2143 · C132
C132 = P41 · P43 · P49
P41 = 24164159986601181377625015589587447765463_<41>
P43 = 2160786218367515171952203262064220489890903_<43>
P49 = 4410527972854632022342616725553254342960601726209_<49>

Number: 132 N=230289472254597723556326237185858964417259744578116480369008481077655245099503360027030457095355662400147348415927381807440279779601 ( 132 digits) SNFS difficulty: 140 digits. Divisors found: r1=24164159986601181377625015589587447765463 (pp41) r2=2160786218367515171952203262064220489890903 (pp43) r3=4410527972854632022342616725553254342960601726209 (pp49) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 11.71 hours. Scaled time: 14.75 units (timescale=1.260). Factorization parameters were as follows: n: 230289472254597723556326237185858964417259744578116480369008481077655245099503360027030457095355662400147348415927381807440279779601 m: 10000000000000000000000000000 c5: 1 c0: 90 skew: 2.46 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1900001) Primes: RFBsize:78498, AFBsize:64158, largePrimes:1620854 encountered Relations: rels:1636099, finalFF:171123 Max relations in full relation-set: 28 Initial matrix: 142720 x 171123 with sparse part having weight 17573423. Pruned matrix : 135646 x 136423 with weight 12496049. Total sieving time: 11.31 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.25 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.71 hours. --------- CPU info (if available) ----------

Jul 11, 2006

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4, GMP-ECM 6.1 B1=11000000
10¹³²+9 = 1(0)₁₃₁9_<133> = 17401 · C128
C128 = P51 · P78
P51 = 411766421379824555923211974201163701971862160573257_<51>
P78 = 139564468173065601765541228336856563574840263361218702800225268893329303849737_<78>

Number: 132 N=57467961611401643583702086087006493879662088385724958335727831733808401815987586920291937244985920349405206597321992988908683409 ( 128 digits) SNFS difficulty: 132 digits. Divisors found: r1=411766421379824555923211974201163701971862160573257 (pp51) r2=139564468173065601765541228336856563574840263361218702800225268893329303849737 (pp78) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.31 hours. Scaled time: 7.55 units (timescale=1.196). Factorization parameters were as follows: n: 57467961611401643583702086087006493879662088385724958335727831733808401815987586920291937244985920349405206597321992988908683409 m: 100000000000000000000000000 c5: 100 c0: 9 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1100001) Primes: RFBsize:63951, AFBsize:63918, largePrimes:1507019 encountered Relations: rels:1497774, finalFF:158693 Max relations in full relation-set: 28 Initial matrix: 127933 x 158693 with sparse part having weight 12991852. Pruned matrix : 119793 x 120496 with weight 8138677. Total sieving time: 6.03 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.16 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.31 hours. --------- CPU info (if available) ----------

10²⁰⁰+9 = 1(0)₁₉₉9_<201> = 27793 · 1619861 · 67747437129266000269703021_<26> · C164
C164 = P39 · P125
P39 = 400259908045666561971192213216134042261_<39>
P125 = 81912816932939583803515921686223425749837243002793830987141671128762200181930502382006509105387526239568992549021452850921893_<125>

Jul 9, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs
10¹⁶⁰+9 = 1(0)₁₅₉9_<161> = 14215681 · 3834622668996503113_<19> · C135
C135 = P32 · P37 · P67
P32 = 49511107570580443175710053727301_<32>
P37 = 1308389305580216069241507311202182597_<37>
P67 = 2831848842389382643911352301752663424041355458316158491328312822249_<67>

Number: template N=3705160740401983100863517084343862366824251826484260212973356231617143408125614337889537228469702200653 ( 103 digits) Divisors found: r1=1308389305580216069241507311202182597 (pp37) r2=2831848842389382643911352301752663424041355458316158491328312822249 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 12.29 hours. Scaled time: 15.45 units (timescale=1.257). Factorization parameters were as follows: name: template n: 3705160740401983100863517084343862366824251826484260212973356231617143408125614337889537228469702200653 skew: 4201.71 # norm 7.68e+013 c5: 90300 c4: -2164338660 c3: -1124179346981 c2: 42838024495449134 c1: 61102231652332890264 c0: -405169698669360292416 # alpha -5.23 Y1: 24804153473 Y0: -33313894859610357733 # Murphy_E 2.50e-009 # M 409331033215913408196436280112604987913307780173380076602933295804435792192031068107187579200174582780 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 [1150000, 1950001) Primes: RFBsize:169511, AFBsize:168711, largePrimes:4431119 encountered Relations: rels:4528620, finalFF:477444 Max relations in full relation-set: 28 Initial matrix: 338303 x 477444 with sparse part having weight 35664560. Pruned matrix : 232265 x 234020 with weight 17071067. Polynomial selection time: 0.70 hours. Total sieving time: 10.32 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.90 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 12.29 hours. --------- CPU info (if available) ----------

10¹⁸⁷+9 = 1(0)₁₈₆9_<188> = 131 · 889796277314453_<15> · 257182844103564007_<18> · C153
C153 = P33 · C120
P33 = 534221796617984999646462038876207_<33>
C120 = [624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287_<120>]
(22·10¹⁸²-1)/3 = 7(3)_182<183> = 89 · 30881 · 50951 · C172
C172 = P30 · P143
P30 = 211784225570152472986757190977_<30>
P143 = 24727131741565022058499972481875489125584547784555429383313765026067944643006887924236480665366530944658610666404211729996682943925108626752731_<143>
(4·10¹⁶⁸-31)/9 = (4)₁₆₇1_<168> = 3 · 31583582440048607_<17> · 1950453510567170479421_<22> · C130
C130 = P26 · P51 · P53
P26 = 40723997197061580454452377_<26>
P51 = 619122012365504891624162034727407775467907313977069_<51>
P53 = 95383354177663653668796178560357826807941934754091677_<53>

Number: template N=59053934184646809250152288479730635440029899839203450505619529839464005477473756144806045588979501754713 ( 104 digits) Divisors found: r1=619122012365504891624162034727407775467907313977069 (pp51) r2=95383354177663653668796178560357826807941934754091677 (pp53) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 12.42 hours. Scaled time: 15.68 units (timescale=1.262). Factorization parameters were as follows: name: template n: 59053934184646809250152288479730635440029899839203450505619529839464005477473756144806045588979501754713 skew: 1584.29 # norm 7.76e+013 c5: 71820 c4: -1805456645 c3: 11521704364278 c2: 6361480388015250 c1: -933919547984490022 c0: -275396482201632940785 # alpha -4.41 Y1: 35687964367 Y0: -60673908364196146748 # Murphy_E 2.20e-009 # M 49808284345992182295493254281137799247143107035608798248782164222227195480358896851882845839564880622878 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 [1150000, 1950001) Primes: RFBsize:169511, AFBsize:170363, largePrimes:4462254 encountered Relations: rels:4584204, finalFF:495463 Max relations in full relation-set: 28 Initial matrix: 339955 x 495463 with sparse part having weight 37585090. Pruned matrix : 225047 x 226810 with weight 17772037. Polynomial selection time: 0.79 hours. Total sieving time: 10.47 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.80 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 12.42 hours. --------- CPU info (if available) ----------

Jul 9, 2006

By Yousuke Koide / GMP-ECM
(10⁹⁰⁹-1)/9 = (1)_909<909> = 3² · 37 · 3637 · 139987 · 333667 · 2096761 · 85556852551_<11> · 272295362253883_<15> · 4531530181816613234555190841_<28> · 759144383635787638836170905729_<30> · 129063282232848961951985354966759_<33> · 18998088572819375252842078421374368604969_<41> · 157793041231623437279937408119546555586267712054762280488959320521697937521092276297325262649574267470228259745983773969571127099146658127611270714291518805884658999061123143366757_<180> · C551
C551 = P34 · C518
P34 = 1612816483312672025726565521114761_<34>
C518 = [18731404609543283232112940354795529905218765028242063904196821320680480327243060323107781513864932349843045574631527371074296472799300221176307921568568002896760698073729122374916147359104494785465229670909538835427313759161196304769503931083522392265590989266657153680618595864394113036876314100827462251460591513613066058256339288827531526049865833183556781227354644105909808435821244299021369213150268134537877336607415598924249317297200399350701289053180044523558985734207417941440449142445239590201068779937245641_<518>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 6, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁶¹-7)/9 = 9(7)_161<162> = 6445832807_<10> · 876136231807637_<15> · C138
C138 = P42 · P96
P42 = 326386964613543818430660282822859481650049_<42>
P96 = 530464933735084358644926407333310225908640242061529220050842604319203486402399066374016158839947_<96>

Number: 97777_161 N=173136839555718845089395520437996758583369835563867385590113997400708115694647626459437368550520023989996609780014966931069180525255707403 ( 138 digits) SNFS difficulty: 163 digits. Divisors found: r1=326386964613543818430660282822859481650049 (pp42) r2=530464933735084358644926407333310225908640242061529220050842604319203486402399066374016158839947 (pp96) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 120.62 hours. Scaled time: 81.06 units (timescale=0.672). Factorization parameters were as follows: name: 97777_161 n: 173136839555718845089395520437996758583369835563867385590113997400708115694647626459437368550520023989996609780014966931069180525255707403 m: 200000000000000000000000000000000 c5: 55 c0: -14 skew: 2 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4950001) Primes: RFBsize:315948, AFBsize:315472, largePrimes:5815005 encountered Relations: rels:5892056, finalFF:708237 Max relations in full relation-set: 28 Initial matrix: 631486 x 708237 with sparse part having weight 49942408. Pruned matrix : 576793 x 580014 with weight 37827629. Total sieving time: 102.75 hours. Total relation processing time: 0.72 hours. Matrix solve time: 16.87 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 120.62 hours. --------- CPU info (if available) ----------

Jul 5, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4
8·10¹⁵¹-3 = 7(9)₁₅₀7_<152> = 7 · 11 · 547 · 773187643 · C139
C139 = P35 · P36 · P69
P35 = 14629262442055574950399532444482723_<35>
P36 = 196829145630461974806359025749407327_<36>
P69 = 853129957804341508281677086652220527996609373987586466237769116989621_<69>

Number: 79997_151 N=2456558048184250863322473394420778738862152389300191605362777223146582956017106437011501898864484201066970818565473010790375814652861561441 ( 139 digits) SNFS difficulty: 152 digits. Divisors found: r1=14629262442055574950399532444482723 (pp35) r2=196829145630461974806359025749407327 (pp36) r3=853129957804341508281677086652220527996609373987586466237769116989621 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 27.22 hours. Scaled time: 16.96 units (timescale=0.623). Factorization parameters were as follows: n: 2456558048184250863322473394420778738862152389300191605362777223146582956017106437011501898864484201066970818565473010790375814652861561441 m: 2000000000000000000000000000000 c5: 5 c0: -6 skew: 1.04 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, 1200000 ) Primes: RFBsize:176302, AFBsize:176493, largePrimes:5630517 encountered Relations: rels:5727860, finalFF:651263 Max relations in full relation-set: 28 Initial matrix: 352860 x 651263 with sparse part having weight 54729852. Pruned matrix : 233396 x 235224 with weight 23367511. Total sieving time: 24.99 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.83 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 27.22 hours. --------- CPU info (if available) ----------

Jul 4, 2006 (3rd)

By Yousuke Koide / GMP-ECM
10⁹¹⁰+1 = 1(0)₉₀₉1_<911> = 29 · 101 · 281 · 421 · 521 · 3541 · 27961 · 2311921 · 3471301 · 13489841 · 121499449 · 13159402621_<11> · 60368344121_<11> · 173827038841_<12> · 654721485601_<12> · 8886004303541_<13> · 19721126575796101_<17> · 131454539198398781_<18> · 527145878168855401_<18> · 1031498834064949381_<19> · 12763852652999774041_<20> · 643852143556794829021_<21> · 848654483879497562821_<21> · 1900381976777332243781_<22> · 12119730504567977254081_<23> · 2737820036624672031089487008281_<31> · 3571618567996393297210217238290456648947344377957590363519828421_<64> · 431916413820617754546053476804635449461410533962843828981966782964481_<69> · 4767139238062537528030092551972140250033930916026378932262992171010636949541765875548467191896982395151649733315765032710728474425304027277684227427428124448895116793267389997296790711552867188304460393677245196360641469741_<223> · C248
C248 = P48 · P200
P48 = 191616955559592384669436097618582851538253404221_<48>
P200 = 60604177158952949654034234379162779182404932436722562911710488710546750366134190897463822800510718962616059662401246546056631138751315004311007246335189571430318613812710829402180309391025505571625641_<200>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 4, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4
(28·10¹⁶⁸-1)/9 = 3(1)_168<169> = 3² · 12377 · 41984093 · C156
C156 = P39 · P118
P39 = 149519217696375701284876859610392404589_<39>
P118 = 4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751_<118>

Number: 31111_168 N=665231561922157233475900748929464114477514261952773705464562504266252579976754133622808054623764706488624353353542718704652248879655622068869216787952344339 ( 156 digits) SNFS difficulty: 169 digits. Divisors found: r1=149519217696375701284876859610392404589 (pp39) r2=4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751 (pp118) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 197.02 hours. Scaled time: 119.59 units (timescale=0.607). Factorization parameters were as follows: n: 665231561922157233475900748929464114477514261952773705464562504266252579976754133622808054623764706488624353353542718704652248879655622068869216787952344339 m: 2000000000000000000000000000000000 c5: 875 c0: -1 skew: 1 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 6800001) Primes: RFBsize:412849, AFBsize:412326, largePrimes:5990289 encountered Relations: rels:6246818, finalFF:925072 Max relations in full relation-set: 28 Initial matrix: 825241 x 925072 with sparse part having weight 51654832. Pruned matrix : 740939 x 745129 with weight 38208626. Total sieving time: 163.63 hours. Total relation processing time: 2.39 hours. Matrix solve time: 30.57 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 197.02 hours. --------- CPU info (if available) ----------

Jul 4, 2006

By wataru sakai / GMP-ECM 6.1 B1=11000000
(4·10¹⁵⁴-31)/9 = (4)₁₅₃1_<154> = 193 · C152
C152 = P33 · P120
P33 = 226956410701884405296554862880163_<33>
P120 = 101465340791608510434494867505301603408393063217871447504733527448696165828183418411522030373903962435273708671186630099_<120>
(4·10¹⁸⁹-31)/9 = (4)₁₈₈1_<189> = 3 · 7 · 59 · 11766674917381365427_<20> · 899820802396378955324797_<24> · C143
C143 = P33 · P111
P33 = 151931647080061133943087045931571_<33>
P111 = 222991415928408701409099236295630310191601638543825165330887266241674230685086304307031418000582086049995350531_<111>

Jul 2, 2006

By Yousuke Koide / GMP-ECM
(10⁸³¹-1)/9 = (1)_831<831> = 3 · 37 · 1016157022810759_<16> · 102092644289739525085919338335107091799_<39> · [10710314284791727138118967000605618050187771277688525854207599641117948350932588043961150274118997769379253719854788136101522618592904749621229242261158372761237323432155862577154173589241914856373487807099618367356448232871_<224>] · C552
C552 = P32 · C521
P32 = 14583704002876908994687648285921_<32>
C521 = [61774491632796531682229129873134854879188889606538991865332732378489613917642712894011233667125452960677817718645793548343784265838763017108563978280693473570714461360003441670259367095714791812784790366631151371036353906505354116538073913505900343716004543484940400938476020223329814783335017162164415847386994139858278658122209555752018698663655721317115426995955226660305071601616168697847105681145122778246346351136132821871465226031104186177624186006825691556823580704133107006746051978806489360025005083661153378671_<521>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 2, 2006

By Wataru Sakai / GMP-ECM 6.1, Msieve v. 1.06, GGNFS-0.77.1-20060513-pentium4 gnfs
(4·10¹⁶¹-31)/9 = (4)₁₆₀1_<161> = 131 · 883 · 2208991 · 797310706397702315094462679_<27> · C123
C123 = P30 · P36 · P58
P30 = 153277297944560404960341396997_<30>
P36 = 193655081371246644974840248683617429_<36>
P58 = 7349490069689279731072870885529978893158946134836342940881_<58>
(4·10¹⁶⁶-31)/9 = (4)₁₆₅1_<166> = 43 · 421 · 11489 · 13063 · 219281 · 2114323 · C142
C142 = P31 · C112
P31 = 1401498638512800602338683574933_<31>
C112 = [2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199_<112>]
(4·10¹⁷¹-31)/9 = (4)₁₇₀1_<171> = 3 · 7² · 8461 · C165
C165 = P35 · P130
P35 = 75940027078135399879289466595503179_<35>
P130 = 4705520875214939206494061499478771720307848518422079127300817212971538067413967160505918436922055101273111247866701496915002960237_<130>
(4·10¹⁷⁴-31)/9 = (4)₁₇₃1_<174> = 3² · 1511 · C170
C170 = P33 · C137
P33 = 598391798346729415087360619163761_<33>
C137 = [54616627017681544743986838092415411816852954873128335763888764844274262889698533737577934396314791125895856004100260211391989572520846519_<137>]
(4·10¹⁷⁶-31)/9 = (4)₁₇₅1_<176> = C176
C176 = P35 · C142
P35 = 11555355372315498456034551118161869_<35>
C142 = [3846220476345118832108998656213957231199997566866995772725881777424686109863785283056075100863623068462636649438105703704881296092597727524989_<142>]
(4·10¹⁸³-31)/9 = (4)₁₈₂1_<183> = 3³ · 7 · 101450189547527_<15> · 5144414891929831963_<19> · C148
C148 = P31 · C118
P31 = 1494159724423093628331262781519_<31>
C118 = [3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351_<118>]
(4·10¹⁹¹-31)/9 = (4)₁₉₀1_<191> = 17 · 79 · 12641819 · C181
C181 = P29 · P37 · P55 · P61
P29 = 46245390417253053507069198277_<29>
P37 = 3288698610155369685906033017650636339_<37>
P55 = 6012569771633282473568788226836503805781988591612498859_<55>
P61 = 2862722471577172119621072059567891400550774220987060325119249_<61>

Number: template N=17212318597180223748039000448764292888344649921197914387046064123268426383453754767791117982035636735387868051436891 ( 116 digits) Divisors found: r1=6012569771633282473568788226836503805781988591612498859 (pp55) r2=2862722471577172119621072059567891400550774220987060325119249 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 58.42 hours. Scaled time: 74.02 units (timescale=1.267). Factorization parameters were as follows: name: template n: 17212318597180223748039000448764292888344649921197914387046064123268426383453754767791117982035636735387868051436891 skew: 91533.13 # norm 1.54e+016 c5: 7980 c4: 4784704672 c3: -222715949872387 c2: -28504304548550969888 c1: 807182662022460227434248 c0: 37026508934687569946500720770 # alpha -6.60 Y1: 284642025107 Y0: -18482745986698681165733 # Murphy_E 5.10e-010 # M 796204495222869985094069394924151158413871914738322193795127044010427633415413290021916171230526019932611113948771 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3570001) Primes: RFBsize:315948, AFBsize:316377, largePrimes:7496042 encountered Relations: rels:7514280, finalFF:746705 Max relations in full relation-set: 28 Initial matrix: 632408 x 746705 with sparse part having weight 56823289. Pruned matrix : 530076 x 533302 with weight 34084002. Polynomial selection time: 3.19 hours. Total sieving time: 46.55 hours. Total relation processing time: 0.52 hours. Matrix solve time: 7.77 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 58.42 hours. --------- CPU info (if available) ----------

(4·10¹⁹⁴-31)/9 = (4)₁₉₃1_<194> = 157 · 983 · 107612863 · 18342123221_<11> · 6108145067228494618057_<22> · 12278415751815556076259294677_<29> · C121
C121 = P39 · P41 · P42
P39 = 101989504789797446295973287236116553803_<39>
P41 = 41521142648191624706188680775787708523349_<41>
P42 = 459382092743332026030965233512572367869779_<42>
(4·10¹⁹⁶-31)/9 = (4)₁₉₅1_<196> = 173 · 8951 · 406573 · C184
C184 = P29 · C156
P29 = 18872789591510503930184653933_<29>
C156 = [374046150228173323380807595022805382554654053940337044029074580835216463679660422954179214722659465000076502672706389982552032900972277554928993940469580563_<156>]

Jul 1, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁵⁹-7)/9 = 9(7)_159<160> = 3 · 103 · 5775893 · C151
C151 = P34 · P117
P34 = 5975646174723226470913875531969593_<34>
P117 = 916806470240261764242266409467665050319996173440276451312922130501690767888779961598648122293529899763384835078305697_<117>

Number: 97777_159 N=5478511076852723780235660847157060648052640735371009236667389281655145464018197502578354313971024281791862019220095682055259107438013227824279762671321 ( 151 digits) SNFS difficulty: 161 digits. Divisors found: r1=5975646174723226470913875531969593 (pp34) r2=916806470240261764242266409467665050319996173440276451312922130501690767888779961598648122293529899763384835078305697 (pp117) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 102.43 hours. Scaled time: 68.83 units (timescale=0.672). Factorization parameters were as follows: name: 97777_159 n: 5478511076852723780235660847157060648052640735371009236667389281655145464018197502578354313971024281791862019220095682055259107438013227824279762671321 m: 100000000000000000000000000000000 c5: 44 c0: -35 skew: 2 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4550001) Primes: RFBsize:315948, AFBsize:316147, largePrimes:5850617 encountered Relations: rels:5997354, finalFF:772910 Max relations in full relation-set: 28 Initial matrix: 632161 x 772910 with sparse part having weight 47864839. Pruned matrix : 522860 x 526084 with weight 32637755. Total sieving time: 88.02 hours. Total relation processing time: 0.71 hours. Matrix solve time: 13.48 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 102.43 hours. --------- CPU info (if available) ----------