20130718, 21:36  #1 
Jun 2012
Boulder, CO
3×59 Posts 
SNFS poly for b^n1, n prime?
Hi,
Does anyone know how to choose good polynomials for factoring values of the form b^n1, where b is fairly large (but not too huge) and n is a small prime? Here's an example: 31280679788951^191. I'm trying the "obvious" sextic. The remaining cofactor is here: http://www.factordb.com/index.php?id...00000626001619 Code:
n: 56345888...6599 m: 30607548590205662094417371657380933049351 type: snfs deg: 6 c6: 31280679788951 c0: 1 * lasieve5 produces output files containing no lines (??) * lasieve4I16e works, but is *abysmally* slow, with a very poor yield. Is there something better out there? 
20130718, 22:40  #2  
Nov 2003
3×13×191 Posts 
Quote:
Consider, e.g. what an "average" norm looks like for the algebraic polynomial. A typical lattice point (say (10^6, 10^6) will have norm 3 x 10^13 x 10^36 ~ 10^49 or so. This is very large; The problem is the coefficient, ~ 3.12 x 10^13. I see no way to get rid of it. Further, the rational side has norms ~ (3.12 x 10^13)^3 x 10^6, ~ 3 x 10^46 which is typical for a C278C280 or so; But the algebraic side is much larger than that for a typical C278. No siever will help. It's the number itself. 

20130718, 22:42  #3 
"Ben"
Feb 2007
2^{6}·3·17 Posts 
You could try the quintic. Suboptimal degree for the size, but much better coefficients.
c5: 1 c0: 31280679788951 m: 957424926574981927749284809890910733899584299547520801 
20130719, 12:14  #4  
Nov 2003
3×13×191 Posts 
Quote:
goes from b^3 to b^4. Thus, the rational norms increase by a factor of b, [big! ~ 10^13] while the algebraic norms only drop by the average value of a lattice point (say 10^6 or so) Going to a quintic should make it WORSE. 

20130719, 13:18  #5  
"Ben"
Feb 2007
2^{6}×3×17 Posts 
Quote:


20130719, 13:39  #6 
Jun 2012
Boulder, CO
3·59 Posts 
The quintic actually does seem to help  if only that lasieve5 isn't choking on it now.
I don't know why lasieve5 produces empty output files for the original sextic that I tried... 
20130719, 17:23  #7 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
2×7×647 Posts 
Try putting a manually picked skew in the sextic poly file?
It is possible that the script that prepares it for you (since it is not in the file) rounds it down to "0". (e.g. printf's it with "%.2f" ?) 
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