Big factors

Jeff Gilchrist · 2013-04-03, 00:53

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

[That's 229.2 bits]

(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.)

dleclair · 2013-04-03, 01:24

Congratulations, Jeff!

ixfd64 · 2013-04-03, 02:05

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

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

[292 bits]

paulunderwood · 2013-04-03, 02:23

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

ixfd64 · 2013-04-03, 02:44

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

Batalov · 2013-04-03, 19:05

Quote:

Originally Posted by paulunderwood

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

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:

Originally Posted by Batalov

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.

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.

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!

2013-04-03, 01:23	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²×23×103 Posts	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 [That's 229.2 bits] (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.)

2013-04-03, 02:20	#5
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22404₈ Posts	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 [292 bits]

2013-04-03, 02:23	#6
paulunderwood Sep 2002 Database er0rr 7233₈ Posts	Vincent TF'd Jeff's Wagstaff candidate to 61 bits Last fiddled with by paulunderwood on 2013-04-03 at 02:29

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2013-04-03, 00:53	#1
Jeff Gilchrist Jun 2003 Ottawa, Canada 3×17×23 Posts	Big factors Found my biggest factor so far for a Wagstaff number: 2^9235649+1 has a factor: 153616228560877782360733142221974579132477827835600631264993134521609 [226.5 bits]

2013-04-03, 01:24	#3
dleclair Mar 2003 7×11 Posts	Congratulations, Jeff!

2013-04-03, 02:05	#4
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 2·5·239 Posts	Have you submitted them to Zimmermann's website? http://www.loria.fr/~zimmerma/records/Pminus1.html

2013-04-03, 02:44	#7
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 956₁₆ Posts	Damn. But it's pretty cool to find a factor that divides into three other ones.

2013-04-03, 19:37	#10
paulunderwood Sep 2002 Database er0rr 3,739 Posts	Oliver has modified his GPU code and Jeff is testing it now. Vincent should be firing up a couple of Teslas soon.

2013-04-07, 11:07	#11
Jeff Gilchrist Jun 2003 Ottawa, Canada 3·17·23 Posts	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!