ECM Factoring for GFNs

[matzetoni]

I saw there are almost no factors registered for GFNs (b^2^N+1) with large N like 16, 17, etc. What software do I have to use in order to find some factors for them? YAFU crashes when I enter such big numbers. Thanks!

[MisterBitcoin]

Originally Posted by matzetoni

I saw there are almost no factors registered for GFNs (b^2^N+1) with large N like 16, 17, etc. What software do I have to use in order to find some factors for them? YAFU crashes when I enter such big numbers. Thanks!

Are you kidding, or is that a typo?
You know about how many digits your talking there, huh?

[matzetoni]

Of course I was just thinking about finding any factors, not factoring these numbers completely.

[axn]

Prime95 / mprime can do ECM & P-1 on these numbers.

PrimeGrid does deep sieving and PRP testing on these numbers, so coordinate with them (if you haven't already) to figure out which ones don't have factors.

[pepi37]

Originally Posted by matzetoni

Of course I was just thinking about finding any factors, not factoring these numbers completely.

1200000033018347521 | 423295908^131072+1
1200000014754250753 | 1434107566^131072+1
1200000058915028993 | 1416413544^131072+1
1200000084461223937 | 1365773326^131072+1
1200000194002812929 | 1275027340^131072+1
1200000206079787009 | 1479080220^131072+1
1200000214073868289 | 374580072^131072+1
1200000262411386881 | 1362834562^131072+1
1200000360969142273 | 581027762^131072+1


Does you need more factors...


Just run opencl sieveless app any enjoy :)


Or if you run Prime95/mprime


271754520^131072+1 has a factor: 1448335003038767382529 (P-1, B1=40000, B2=500000)
271754590^131072+1 has a factor: 62066673049552736747521 (P-1, B1=40000)
271754588^131072+1 has a factor: 3785032735161581569 (P-1, B1=40000, B2=500000)
271700578^131072+1 has a factor: 6633353454338703361 (P-1, B1=25000)

[MisterBitcoin]

Originally Posted by matzetoni

Of course I was just thinking about finding any factors, not factoring these numbers completely.

Give it a try and pick some random number in a digit range (above ~1500 digits when you want to use YAFU); and try if you can find some factors.

Special forms like n^m-1 or n^m+1 will give you many. Just search for them. :)


It would be nice to find some more people "cleaning" up the composite list. >>

[matzetoni]

Originally Posted by MisterBitcoin

Give it a try and pick some random number in a digit range (above ~1500 digits when you want to use YAFU); and try if you can find some factors.

Special forms like n^m-1 or n^m+1 will give you many. Just search for them. :)


It would be nice to find some more people "cleaning" up the composite list. >>

Has there been any greater interest / effort in factoring GFNs (b^2^N+1 form) in the past? I just don't want to duplicate work.

[matzetoni]

I'm going for smaller numbers now which can be factored in reasonable time, e.g. I factored a C104 cofactor of 2*3^306+1 in 3.5 h:


P56 = 32164135493155426933135767708550436931390657201593485721
P49 = 1522525026464068699495246003230848523594670181147


(using yafu -> factor)

[LaurV]

Originally Posted by matzetoni

e.g. I factored a C104 cofactor of 2*3^306+1 in 3.5 h

What rig is that? How many cores/threads? It looks kinda slow... Have you run "yafu -tune"?

[matzetoni]

What rig is that? How many cores/threads? It looks kinda slow... Have you run "yafu -tune"?

Yes, I ran tune once a few days ago. I was only running one thread on an older machine, while running some prime search programs, so yes it was slow...