News and updates, December 2005

News and updates, December 2005	2006-01-01(Sun) 15:36

Dec 30, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(2·10¹⁵¹+43)/9 = (2)₁₅₀7_<151> = 7 · 24749 · 18201677391168885163267_<23> · C123
C123 = P40 · P84
P40 = 1585382450759782582185874826963629040021_<40>
P84 = 444514908669606312113740192443485361556662962048015388348253890530047576482332604727_<84>

Number: 22227_151
N=704726135305881380763457905432516149604684708960469500046876760389060373827717286927921031365688899072885646461907456779267
  ( 123 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1585382450759782582185874826963629040021 (pp40)
 r2=444514908669606312113740192443485361556662962048015388348253890530047576482332604727 (pp84)
Version: GGNFS-0.77.1
Total time: 40.28 hours.
Scaled time: 24.05 units (timescale=0.597).
Factorization parameters were as follows:
name: 22227_151
n: 704726135305881380763457905432516149604684708960469500046876760389060373827717286927921031365688899072885646461907456779267
m: 1000000000000000000000000000000
c5: 20
c0: 43
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2200001)
Relations: rels:5286269, finalFF:407284
Initial matrix: 352666 x 407284 with sparse part having weight 36430728.
Pruned matrix : 342380 x 344207 with weight 24722093.
Total sieving time: 35.20 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 4.64 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 40.28 hours.
 --------- CPU info (if available) ----------

Dec 29, 2005

By Yousuke Koide / GMP-ECM
(10⁸⁶⁷-1)/9 = (1)₈₆₇_<867> = 3 · 37 · 613 · 42773 · 210631 · 2071723 · 52986961 · 93101929 · 1112647111_<10> · 5363222357_<10> · 234771432523_<12> · 6270681177984151_<16> · 13168164561429877_<17> · 93195753455238027770502373_<26> · 25086158646798685749029022942725879293529996353937930044688310225209792405267161387550045665503080767367139652501504645587640324255739525766942448322852994756555563269219516158897234150632016254115138596672215506548424356751044570760748443769_<242> · C500
C500 = P35 · C465
P35 = 74451201112778571232641337987561693_<35>
C465 = [880749077926577843124022815543905243436243176981401822934212608916166210959442844004644678747282196938320657996123515308248887369738488527950161888653706681327573251104889523953376829693033793283094622861344739155192294195184259873540811658992698965037197713469231389139638849886390678504680208926869468306142739078126584537647973856670716121049791242618239094923624268494318233201634115438047557084451257111644843007270532012304405353201017823761171061173636448711_<465>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 28, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁷²+17)/9 = (1)₁₇₁3_<172> = 3 · 7 · 72168249258114728606726201031397_<32> · C138
C138 = P56 · P83
P56 = 63400031508097228233880422309192926529285713463921363067_<56>
P83 = 11563852734794061499333658649310855699552076107764096814479223746909899650565236147_<83>

Number: 11113_172
N=733148627740939799927300997517632842383966933831900770855308243545825232400868389092834346740014256341748837898283664204679161320979182849
  ( 138 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=63400031508097228233880422309192926529285713463921363067 (pp56)
 r2=11563852734794061499333658649310855699552076107764096814479223746909899650565236147 (pp83)
Version: GGNFS-0.77.1
Total time: -596245.03 hours.
Scaled time: -396502.95 units (timescale=0.665).
Factorization parameters were as follows:
name: 11113_172
n: 733148627740939799927300997517632842383966933831900770855308243545825232400868389092834346740014256341748837898283664204679161320979182849
m: 10000000000000000000000000000000000
c5: 100
c0: 17
skew: 3
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [3000000, 9100001)
Relations: rels:6487146, finalFF:930680
Initial matrix: 825809 x 930680 with sparse part having weight 68493812.
Pruned matrix : 788756 x 792949 with weight 49116979.
Total sieving time: -596270.61 hours.
Total relation processing time: 1.42 hours.
Matrix solve time: 23.87 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: -596245.03 hours.
 --------- CPU info (if available) ----------

Note: The informations of the elapsed time are something wrong. Corrected sieving time is 252.63 hours and total time is 278.21 hours.

Dec 24, 2005

The repunit factor tables, Factorizations of 11...11 (Repunit) and Factorizations of 100...001, were updated in response to the changes of Factorizations of Repunit Numbers maintained by Yousuke Koide. There are more than 300 factors which have been imported and four corrected factorizations; (10¹⁴⁸⁸-1)/9, (10¹⁶²⁶-1)/9, 10¹¹¹⁶+1 and 10¹⁸⁶⁰+1.

Dec 15, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁷²+53)/9 = (1)₁₇₁7_<172> = C172
C172 = P61 · P111
P61 = 1820564273244167614352936931494044490043637812425486039550179_<61>
P111 = 610311389408492932205757446216163980731782153242779699711015601594898956611692200384114483457561447170835483023_<111>

Number: 11117_172
N=1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 172 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=1820564273244167614352936931494044490043637812425486039550179 (pp61)
 r2=610311389408492932205757446216163980731782153242779699711015601594898956611692200384114483457561447170835483023 (pp111)
Version: GGNFS-0.77.1
Total time: 324.90 hours.
Scaled time: 216.06 units (timescale=0.665).
Factorization parameters were as follows:
name: 11117_172
n: 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 10000000000000000000000000000000000
c5: 100
c0: 53
skew: 3
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [3000000, 10500001)
Relations: rels:6689497, finalFF:941034
Initial matrix: 825039 x 941034 with sparse part having weight 80343340.
Pruned matrix : 789261 x 793450 with weight 57498680.
Total sieving time: 297.79 hours.
Total relation processing time: 2.20 hours.
Matrix solve time: 24.62 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 324.90 hours.
 --------- CPU info (if available) ----------

Dec 1, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁶⁷+53)/9 = (1)₁₆₆7_<167> = 367 · 3779 · C160
C160 = P41 · P120
P41 = 72180524179814281371646723253295317425753_<41>
P120 = 110992722143284079668473710836385761364736707416721224780341636632728276454533977666549953684709379743979990569220351273_<120>

Number: 11117_167
N=8011512864446724521005665982243122656982990837152621803636698080609759448718185981983549640174916962672038225812020906523510545594441035545720622363160756533569
  ( 160 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=72180524179814281371646723253295317425753 (pp41)
 r2=110992722143284079668473710836385761364736707416721224780341636632728276454533977666549953684709379743979990569220351273 (pp120)
Version: GGNFS-0.77.1
Total time: 191.80 hours.
Scaled time: 127.74 units (timescale=0.666).
Factorization parameters were as follows:
name: 1111_167
n: 8011512864446724521005665982243122656982990837152621803636698080609759448718185981983549640174916962672038225812020906523510545594441035545720622363160756533569
m: 1000000000000000000000000000000000
c5: 100
c0: 53
skew: 3
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2500000, 6900001)
Relations: rels:6266779, finalFF:815614
Initial matrix: 696598 x 815614 with sparse part having weight 65714425.
Pruned matrix : 662725 x 666271 with weight 43445378.
Total sieving time: 173.36 hours.
Total relation processing time: 0.74 hours.
Matrix solve time: 17.46 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 191.80 hours.
 --------- CPU info (if available) ----------