[quote=fivemack;110154]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]

Ok. Nowtime I'm trying to make a general formula for creating polynomilas for factoring integers of a^b+(-)c^b form. Do you know this formula (algorithm)?

[QUOTE=VolMike;110158]Ok. Nowtime I'm trying to make a general formula for creating polynomilas for factoring integers of a^b+(-)c^b form. Do you know this formula (algorithm)?[/QUOTE]

Yes, I do.

Read my paper.

[quote=R.D. Silverman;110161]Yes, I do.

Read my paper.[/quote]
I'm found some press-clippings of yuor book, there are no information about general algorith for creating polymons. Thus, I hope that somebody could give me a brief explanation of main ideas.

[QUOTE=VolMike;110172]I'm found some press-clippings of yuor book, there are no information about general algorith for creating polymons. Thus, I hope that somebody could give me a brief explanation of main ideas.[/QUOTE]

There's a line from a pop song two or three summers ago that might
be of relevance here. It goes "wanna know the rest? ... buy the rights!".
I forget the precise name of the group, something about a million dollar
club. Catchy lyric. Why not at least ask for copy of the paper, instead
of for an "executive summary"? -bd

[QUOTE=VolMike;110172]I'm found some press-clippings of yuor book, there are no information about general algorith for creating polymons. Thus, I hope that somebody could give me a brief explanation of main ideas.[/QUOTE]

Minor correction: it was not a book.


You could also look at the paper by
Elkenbracht-Huizing, Montgomery, Silverman, Wackerbarth, & Wagstaff
"The Number Field Sieve on Many Computers", Proc. 5th Conf. Canadian
No. Thr. Assoc.

It discusses many aspects of SNFS polynomial selection.

[quote=bdodson;110175]There's a line from a pop song two or three summers ago that might
be of relevance here. It goes "wanna know the rest? ... buy the rights!".
I forget the precise name of the group, something about a million dollar
club. Catchy lyric. Why not at least ask for copy of the paper, instead
of for an "executive summary"? -bd[/quote]

I appreciate you irony;prefer listening new age.

[quote=bdodson;110175]There's a line from a pop song two or three summers ago that might
be of relevance here. It goes "wanna know the rest? ... buy the rights!".
I forget the precise name of the group, something about a million dollar
club. Catchy lyric. Why not at least ask for copy of the paper, instead
of for an "executive summary"? -bd[/quote]

OMC, "How Bizarre"
[URL]http://www.anysonglyrics.com/lyrics/o/omc/howbizarre.htm[/URL]

[quote=jasonp;110147]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.

[/quote]

yes...the polys are [TEX]a^2x^4\pm2abx^2+b^2[/TEX] (splits modulo every prime)and[TEX]\frac{x^5\pm1}{x\pm1}[/TEX].

[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]

Your poly file for 7,3,192+:
[CODE]n: <insert the composite here>
# 7^192+3^192, difficulty: 108.17, skewness: 1.00, alpha: 1.29
# cost: 1.05404e+013, est. time: 0.01 GHz days (not accurate yet!)
skew: 1.000
c4: 1
c2: -1
c0: 1
Y1: 1853020188851841
Y0: -1104427674243920646305299201
type: snfs
[/CODE]
generated by akruppa's phi program.

For other parameters, see def-par.txt in ggnfs....

[quote=wpolly;110193]Your poly file for 7,3,192+:
[code]n: <insert the composite here>
# 7^192+3^192, difficulty: 108.17, skewness: 1.00, alpha: 1.29
# cost: 1.05404e+013, est. time: 0.01 GHz days (not accurate yet!)
skew: 1.000
c4: 1
c2: -1
c0: 1
Y1: 1853020188851841
Y0: -1104427674243920646305299201
type: snfs
[/code]generated by akruppa's phi program.

For other parameters, see def-par.txt in ggnfs....[/quote]
Thank's Wpolly!

[QUOTE=R.D. Silverman;110177]Minor correction: it was not a book.


You could also look at the paper by
Elkenbracht-Huizing, Montgomery, Silverman, Wackerbarth, & Wagstaff
"The Number Field Sieve on Many Computers", Proc. 5th Conf. Canadian
No. Thr. Assoc.

It discusses many aspects of SNFS polynomial selection.[/QUOTE]

This paper can be found on-line. It turned up after a short
search on google.