Factorizations achieved with the GGNFS software
I have removed most of the smaller examples to make room for some slightly
more interesting ones. GGNFS is not quite upto an interesting point yet,
but it has been used to factor some SNFS 100-150 digit numbers from
the lists at
http://homepage2.nifty.com/m_kamada/math/factorizations.htm.
Note that I am neglecting the time for polynomial selection. In reality, though,
this is not a negligible step! But for the size numbers we're at right now, it is.
Also, note that parameter selection was not necessarily optimal for these
numbers!
Finally: These are literal timings, from a 3200+ Athlon XP. Also note that these
are in `calander' time, not processor time. But I think most of them are pretty
much on the money.
| GGNFS Version: GGNFS-0.30.0 |
| tstS2: n= | (7^135 - 26)/17189077 |
| Digits: | 107 |
| Poly: | x^4 - 182 |
| Factor base: | 50000/50003, 2LP, limit=40000000 |
| Sieve region: | rectangular, a=[-2500000, 2500000] b=[1,100000] (10.4 hours) |
| relations: | 1172696 total (32620 full), net: 102478 full relations. (2 hours) |
| Matrix: | 100067 x 102478 with 3452639 nonzero entries. | Pruned matrix: | 96830 x 98799 with 3241549 nonzero entries (22.5 minutes) | Square root: | 50 seconds. |
| Divisor 1: | 57193416059866787056849810562654593428856404939606205039438841736303370248749 |
| Divisor 2: | 1246340787605505082446220854829 |
| Total time: | 12.8 hours |
| GGNFS Version: GGNFS-0.41.0 |
| tst300: n= | 96693117801151196901759163062845005740662686097142800237507655454506720219714304894194857 |
| Digits: | 89 |
| Poly: | 472142462220X^4 + 48092877789426X^3 -20683531137072628X^2 + 933616521383962703X + 19869490475668857650 |
| Factor base limits | 600000/700000, LP limits 2^{25}/2^{25} |
| Sieve region: | Lattice only: q in [700000, 1180000] (2.7 hours). |
| relations: | 1277447 total, net: 118457 full relations. (.4 hours) |
| Matrix: | 105728 x 118457 with weight 10223244 |
| Pruned matrix: | 103664 x 105770 with weight 8272947 (solve time: 0.8 hours) |
| Square root: | .15 hours. |
| Divisor 1: | 743507790479100314596230492599016928949651051 |
| Divisor 2: | 130049905380069045841413544182676651433512507 |
| Total time: | 4.1 hours |
| GGNFS Version: GGNFS-0.40.2 |
| tst_DB_AL: n= | (2^488+1)/257 (previously done by Bernstein, Lenstra in 1992 on a MasPar). |
| Digits: | 144 |
| Poly: | x^5+4 |
| Factor base limits: | 1300000/1300000, 2LP, limit=2^27 / 2^27 |
| Sieve region: | lattice only, N(q)=1300000...2933283 |
| relations: | total: 3685822, final fulls:211934 (29.0 hours) |
| Matrix: | 199913 x 211934 with weight 21344779 |
| Pruned matrix: | 198205 x 202202 with weight 19631555 (solve time 2.75 hours) |
| Square root: | 0.1 hours. |
| Divisor 1: | 1035817877926014488587133818491976759389034764353 |
| Divisor 2: | p_97 |
| Total time: | 33 hours |
| GGNFS Version: GGNFS-0.50.2 |
| rsa100: n= | 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 |
| Digits: | 100 |
| Poly: | 11834320x^5 + 7237710664x^4 - 23461090705819x^3 - 4934660279943864x^2
+ 2161879914274565376x + 58428541449830190267 |
| Factor base limits: | 1100K/1100K, 2LP, limit=2^26 / 2^26 |
| Sieve region: | lattice only, N(q)=1100000...3500000 (14.8.0 hours) |
| relations: | total: 2443980, final fulls:182902 (0.8 hours) |
| Matrix: | 171666 x 182902 with weight 23988332 |
| Pruned matrix: | 161107 x 161310 with weight 20802635 (solve time 2.0 hours) |
| Square root: | 0.3 hours. |
| Divisor 1: | 37975227936943673922808872755445627854565536638199 |
| Divisor 2: | 40094690950920881030683735292761468389214899724061 |
| Total time: | 18 hours |
| GGNFS Version: GGNFS-0.54.4 |
| rsa110: n= | 35794234179725868774991807832568455403003778024228226193532908190484670252364677411513516111204504060317568667 |
| Digits: | 110 |
| Poly: | 423645600x^5 + 184792454222x^4 - 401523870222664x^3 + 917216805280379393x^2
-189354398484955516596x + 7227485970292708793872 |
| Factor base limits: | 3M/3M, 2LP, limit=2^26 / 2^26 |
| Sieve region: | lattice only, N(q)=3M..9.4M (50 hours) |
| relations: | total: 3.5M, final fulls:439221 (1.8 hours) |
| Matrix: | 433833 x 439221 |
| Pruned matrix: | 418129 x 418594 (solve time 6.0 hours) |
| Square root: | 0.8 hours. |
| Divisor 1: | 5846418214406154678836553182979162384198610505601062333 |
| Divisor 2: | 6122421090493547576937037317561418841225758554253106999 |
| Total time: | 58 hours |
|