Discussion related to cado-nfs

[eric.jeancolas@free.fr]

Hello,

I've got a problem similar to some entries under sqrt freeze. Indeed, it's more a loop than a freeze in my case, as CPU is running 100% of available CPU, and Mem is frozen to a definite number, rather low.
The number I wanted to factorize is 10^264-8. After some trivial factors, the remaining number to factorize is a c172.

If I use the SNFS polynomial

n: 1076055610553953428313175224895622605776266517453622003185124607239702147806998665691043128308871002453406792063013816554039512762019541169887659794258167262084104506520897
skew: 0.14
type: snfs
c0: 1
c2: 50
c4: 2500
Y0: 10000000000000000000000000000000000000000000
Y1: -1
# f(x) = 2500*x^4+50*x^2+1
# g(x) = -x+10000000000000000000000000000000000000000000

I get a  loop in the step 2 of the sqrt process.

If I use the SNFS polynomial

n: 1076055610553953428313175224895622605776266517453622003185124607239702147806998665691043128308871002453406792063013816554039512762019541169887659794258167262084104506520897

skew: 0.58

type: snfs

c0: 1

c3: 5

c6: 25

Y0: 100000000000000000000000000000

Y1: -1

# f(x) = 25*x^6+5*x^3+1

# g(x) = -x+100000000000000000000000000000

the factorization is done ok.

So, of course, there is an answer : use degree 6 polynomial instead of degree 4 ;-) 

But I think it may be helpful to understand what's going on, and maybe to issue an error exit with an error message instead of the loop.

I made tests in cado-nfs-2.3.0 and cado-nfs-3.0.0 (one I downloaded at least one year ago), with 2 different computers, one with 8Gb of RAM and one with 16Gb of RAM. But with tasks.sqrt.threads=1, the memory usage in TOP display is frozen at 2.2 % when the loop occurs on my 16Gb computer...

I can PM you whatever you need. You may also compute it if you have available computer power, both SFNS polynomials are rather efficient, deg 6 being even more efficient than deg 4. It takes roughly 1 day of computation time on a 4-core computer.

Best regards.