7,8,192+ factored. An ECM miss...

[CODE]
Number: 7_8_192P
N=14025343060547284197216173230192158522023971240484924173118834493918030294625110653150769039523001089
( 101 digits)
SNFS difficulty: 115 digits.
Divisors found:
r1=18003398404623390927915853128994177 (pp35)
r2=779038642890082574808892048783504611971833230172988543825129629057 (pp66)
[/CODE]

found on the 18th dependency...the previous ones all gave the "f appears to split modulo all primes" warning.

[quote=wpolly;109971]7,8,192+ factored. An ECM miss...

[code]
Number: 7_8_192P
N=14025343060547284197216173230192158522023971240484924173118834493918030294625110653150769039523001089
( 101 digits)
SNFS difficulty: 115 digits.
Divisors found:
r1=18003398404623390927915853128994177 (pp35)
r2=779038642890082574808892048783504611971833230172988543825129629057 (pp66)
[/code]found on the 18th dependency...the previous ones all gave the "f appears to split modulo all primes" warning.[/quote]

What program did you use and how much time did factorzation take?

[QUOTE=VolMike;109990]What program did you use and how much time did factorzation take?[/QUOTE]
ggnfs, 2.59 hours

[quote=wpolly;110041]ggnfs, 2.59 hours[/quote]
All steps of GNFS factorization on 1 machine for 101 digits number took 2.59 hours?
Could you give me the links to executable files of ggnfs for Windows platform?

[quote=VolMike;110075]All steps of GNFS factorization on 1 machine for 101 digits number took 2.59 hours?
[/quote]

Yes, every step. 115-digit [B]SNFS[/B] is next to trivial these days.

[QUOTE]Could you give me the links to executable files of ggnfs for Windows platform?[/QUOTE][URL="http://sourceforge.net/projects/ggnfs"]sourceforge[/URL] have win32-binaries, but it(namely, the 20060513 snapshot) still suffer form the "odd exponent" bug.....

9,5,155+.c115 factored.

[CODE]
Number: 5_9_155P
N=4770791007766606203473047168886164696138214081999005213731610975404427089546078494266223812693070458877726745435121
( 115 digits)
SNFS difficulty: 118 digits.
Divisors found:
r1=22115320670870567175220774112072111620498561 (pp44)
r2=215723347572821088022116709239319889266594833857297588853654519541038961 (pp72)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 3.30 hours.
Scaled time: 2.17 units (timescale=0.656).

[/CODE]

This time it's found on dependency 17...

Most of the failed deps give beta^2=0..is it normal to have this or there's still some bugs in sqrt:question:

[QUOTE=wpolly;110124]
This time it's found on dependency 17...

Most of the failed deps give beta^2=0..is it normal to have this or there's still some bugs in sqrt:question:[/QUOTE]
Certain unusual SNFS polynomials can cause this behavior, the log message you mentioned previously indiciates you're dealing with them. Are these degree 4 polynomials? It's more common in that case.

msieve also has trouble with these kinds of problems, but appears to need fewer dependencies to complete the factorization than GGNFS does. It probably isn't worth switching tools for these small kinds of problems.

[quote=wpolly;110124]9,5,155+.c115 factored.

[code]
Number: 5_9_155P
N=4770791007766606203473047168886164696138214081999005213731610975404427089546078494266223812693070458877726745435121
( 115 digits)
SNFS difficulty: 118 digits.
Divisors found:
r1=22115320670870567175220774112072111620498561 (pp44)
r2=215723347572821088022116709239319889266594833857297588853654519541038961 (pp72)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 3.30 hours.
Scaled time: 2.17 units (timescale=0.656).

[/code]This time it's found on dependency 17...

Most of the failed deps give beta^2=0..is it normal to have this or there's still some bugs in sqrt:question:[/quote]

Marvellous!
How do you choose the optimal parameters for SNFS factorization? (In ggns-doc there is an[COLOR=#808080] roughly description of choosing parameters; may be you know enough optimal for SNFS factoring numbers of special forms in range of 100-130 digits[/COLOR]...)

[QUOTE=VolMike;110150]Marvellous!
How do you choose the optimal parameters for SNFS factorization? (In ggns-doc there is an[COLOR=#808080] roughly description of choosing parameters; may be you know enough optimal for SNFS factoring numbers of special forms in range of 100-130 digits[/COLOR]...)[/QUOTE]

How? You read my paper:

R. Silverman
Optimal Parameterization of SNFS
J. Math. Cryptology Vol 1 2007.

For numbers this small, you write a 7+3_192.poly file and then feed it to tests/factLat.pl, which uses vaguely reasonable parameters.

On the other hand, factLat.pl seems to be fitted data rather than modelled data: for large problems (say >180-digit SNFS and >125-digit GNFS) it uses parameters for 180-digit SNFS and 125-digit GNFS, which are very bad (small_prime too small).

For larger numbers, I tend to assume that the number of relations you need is around 2^{large prime bound - 4}, then try various small-prime and large-prime bounds to see which would in principle generate that number of relations fast enough ... relation-production rate does go down a bit as Q goes up, so you can't just extrapolate from a figure at Q=2e7 all the way to Q=5e7, but you can do a run at 2e7, see that you need about 3e7 Qs, and then see what the rate is like at 3.5e7 and 5e7.

It is much worse to have small_prime too small than too large.

[quote=R.D. Silverman;110152]How? You read my paper:

R. Silverman
Optimal Parameterization of SNFS
J. Math. Cryptology Vol 1 2007.[/quote]
Thank's!