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 Jeff Gilchrist 2013-04-03 00:53

Big factors

Found my biggest factor so far for a Wagstaff number:

2^9235649+1 has a factor: 153616228560877782360733142221974579132477827835600631264993134521609 [226.5 bits]

 Batalov 2013-04-03 01:23

worktodo.txt:
Pminus1=1,2,8232929,1,10000,0,"3"
=>

[CODE]P-1 found a factor in stage #1, B1=10000.
2^8232929+1 has a factor: 997183410304432117267065463213026379715216410911450070172292068758243
[/CODE]
[That's 229.2 bits]
[SPOILER]
(Of course, I cheated in Pari first, by finding a few 2^p+1 that have at least five small factors. This one has two more slightly larger. Seven altogether.)
[/SPOILER]

 dleclair 2013-04-03 01:24

Congratulations, Jeff!

 ixfd64 2013-04-03 02:05

Have you submitted them to Zimmermann's website?
[url]http://www.loria.fr/~zimmerma/records/Pminus1.html[/url]

 Batalov 2013-04-03 02:20

Composite factors are not eligible:
153616228560877782360733142221974579132477827835600631264993134521609
= 7160401272398244691 * 219902328863708115073 * 97559577016295905770143558963
The smallest of them should have been found by TF, easily: 62 bits. (Wagstaff numbers have factors of form 2kp+1, just like Mersenne's.)

Let's find some even larger factors...
[CODE]P-1 found a factor in stage #1, B1=100000.
2^8232929+1 has a factor: 8203927240046868961280630569987984778892578839825012457683394506843242760078451651993971
[/CODE]
[292 bits]

 paulunderwood 2013-04-03 02:23

Vincent TF'd Jeff's Wagstaff candidate to 61 bits :smile:

 ixfd64 2013-04-03 02:44

Damn. But it's pretty cool to find a factor that divides into three other ones. :smile:

 Batalov 2013-04-03 19:05

[QUOTE=paulunderwood;335928]Vincent TF'd Jeff's Wagstaff candidate to 61 bits :smile:[/QUOTE]
Isn't it fairly obvious to use a slightly revised mfaktc for that?

This is how far you guys TF? 61 bits? This is very low.

 Mini-Geek 2013-04-03 19:23

[QUOTE=Batalov;335988]Isn't it fairly obvious to use a slightly revised mfaktc for that?

This is how far you guys TF? 61 bits? This is very low.[/QUOTE]

Don't forget that TF to 61 bits for a number with p=9M is much harder than TF to 61 with p=64M. I think it's more like TFing p=64M to 64 bits...that still seems low, but for p=9M, maybe that's sufficient. Maybe they don't have an mfaktc equivalent. ("wfaktc"?)

 paulunderwood 2013-04-03 19:37

Oliver has modified his GPU code and Jeff is testing it now. Vincent should be firing up a couple of Teslas soon. :smile:

 Jeff Gilchrist 2013-04-07 11:07

As Paul said, we are factoring to high bits now with the modified version of mfaktc. That P-1 factor was from the last batch of p-1 before I started using it.

GPU TF FTW!

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