What Murphy score to expect or need [cado-nfs]

kosta · 2013-04-17, 00:27

What Murphy score can I expect for a 181 digit composite? So far Cado reports going over 26% of the region it wants to search and I got one with 1.17*10E-14
It is by the way 40% better than most other found so far. Is this likely to be good enough?

I now realize I bit off a little bit more than i can easily chew. I was fooled after observing that record factorizations were much much bigger, and when Dubslow factored a number I wanted of more than 212 digits in 10 days. I've been running polyselect already for more than a week on an 8core machine of 2008 vintage. :-(

K

Batalov · 2013-04-17, 00:40

You would need ~2000 CPU-days to sieve this project, are you sure that you are ready for this? (it is roughly equivalent to a SNFS-270-digit project)

If CADO calcluated E-value is not very different from msieve's, then you should expect a much higher E, possibly 9e-14 ... 1e-13.

kosta · 2013-04-17, 15:02

Thanks, Sergei, actually i made a mistake caused by frustration. This is a 191 digit number actually, so it would take even longer than that. But it is a factor of M61^16+1 which is 294 digits. (a few factors of 103 digits in total already have been taken off by ECM). Because this was much more than the remaining composite number I thought the SNFS form of it would be useless. But thanks for pointing out that the SNFS equivalent difficulty is about the same.

Could you confirm for me that I should go for SNFS which comes from the 294 digit parent vs GNFS with 191 digits. Does it matter that 294 > 280 ?

If I get totally frustrated at some point I may ask people to help sieving, but for now I will put effort to make sure I undertsand what I'm doing, and also try obtain some cpu's.

Batalov · 2013-04-17, 17:30

191-digit GNFS is better than the 294-digit SNFS. It's a GNFS job.

You would expect a poly with E ~= 2e-14 for this input. Sieving would take ~6000 CPU days and the matrix would be quite hard to finish on a home-computer (rough guess is that less than 16Gb won't work).

This would be a project of the distributed type.

2013-04-17, 00:27	#1
kosta Jan 2013 56₁₀ Posts	What Murphy score to expect or need [cado-nfs] What Murphy score can I expect for a 181 digit composite? So far Cado reports going over 26% of the region it wants to search and I got one with 1.17*10E-14 It is by the way 40% better than most other found so far. Is this likely to be good enough? I now realize I bit off a little bit more than i can easily chew. I was fooled after observing that record factorizations were much much bigger, and when Dubslow factored a number I wanted of more than 212 digits in 10 days. I've been running polyselect already for more than a week on an 8core machine of 2008 vintage. :-( K

2013-04-17, 15:02	#3
kosta Jan 2013 38₁₆ Posts	Thanks, Sergei, actually i made a mistake caused by frustration. This is a 191 digit number actually, so it would take even longer than that. But it is a factor of M61^16+1 which is 294 digits. (a few factors of 103 digits in total already have been taken off by ECM). Because this was much more than the remaining composite number I thought the SNFS form of it would be useless. But thanks for pointing out that the SNFS equivalent difficulty is about the same. Could you confirm for me that I should go for SNFS which comes from the 294 digit parent vs GNFS with 191 digits. Does it matter that 294 > 280 ? If I get totally frustrated at some point I may ask people to help sieving, but for now I will put effort to make sure I undertsand what I'm doing, and also try obtain some cpu's. Last fiddled with by kosta on 2013-04-17 at 15:03

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2013-04-17, 00:40	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10,061 Posts	You would need ~2000 CPU-days to sieve this project, are you sure that you are ready for this? (it is roughly equivalent to a SNFS-270-digit project) If CADO calcluated E-value is not very different from msieve's, then you should expect a much higher E, possibly 9e-14 ... 1e-13.

2013-04-17, 17:30	#4
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10,061 Posts	191-digit GNFS is better than the 294-digit SNFS. It's a GNFS job. You would expect a poly with E ~= 2e-14 for this input. Sieving would take ~6000 CPU days and the matrix would be quite hard to finish on a home-computer (rough guess is that less than 16Gb won't work). This would be a project of the distributed type.