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Old 2013-04-03, 00:53   #1
Jeff Gilchrist
 
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Default Big factors

Found my biggest factor so far for a Wagstaff number:

2^9235649+1 has a factor: 153616228560877782360733142221974579132477827835600631264993134521609 [226.5 bits]
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Old 2013-04-03, 01:23   #2
Batalov
 
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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.)
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Old 2013-04-03, 01:24   #3
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Congratulations, Jeff!
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Old 2013-04-03, 02:05   #4
ixfd64
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Have you submitted them to Zimmermann's website?
http://www.loria.fr/~zimmerma/records/Pminus1.html
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Old 2013-04-03, 02:20   #5
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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]
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Old 2013-04-03, 02:23   #6
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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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Old 2013-04-03, 02:44   #7
ixfd64
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Damn. But it's pretty cool to find a factor that divides into three other ones.
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Old 2013-04-03, 19:05   #8
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Quote:
Originally Posted by paulunderwood View Post
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.
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Old 2013-04-03, 19:23   #9
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Quote:
Originally Posted by Batalov View Post
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"?)
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Old 2013-04-03, 19:37   #10
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Oliver has modified his GPU code and Jeff is testing it now. Vincent should be firing up a couple of Teslas soon.
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Old 2013-04-07, 11:07   #11
Jeff Gilchrist
 
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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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