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Old 2009-07-18, 00:49   #1
Prime95
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Default GIMPS' first Fermat factor!

User Buckle turned in this gem recently!

F19 has a factor: 37590055514133754286524446080499713

Anyone want to test if this completes the factorization of F19?
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Old 2009-07-18, 01:02   #2
akruppa
 
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Congratulations! This is truly a rare discovery. It's the first factor of a Fermat number of index < 30 since the turn of the century, and only the fourth of index < 80. For comparison, GIMPS found 9 Mersenne primes in the same time frame.

How would one test the primality with Prime95/mprime? With a PRP line in worktodo? Can you specify the known factors like you can for ECM?

Alex
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Old 2009-07-18, 01:02   #3
mdettweiler
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Quote:
Originally Posted by Prime95 View Post
User Buckle turned in this gem recently!

F19 has a factor: 37590055514133754286524446080499713

Anyone want to test if this completes the factorization of F19?
Per factordb.com, a 15,770-digit composite cofactor remains.

Edit: Regarding the primality of the factor, that has also been automatically proven by the above-linked website upon submission of the factor.

Edit2: scratch all that, I just remembered that when a number shows up in bright red on factordb.com, it means that it was too big to be tested for primality or even PRPed.

Last fiddled with by mdettweiler on 2009-07-18 at 01:04
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Old 2009-07-18, 01:02   #4
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Quote:
Originally Posted by Prime95 View Post
User Buckle turned in this gem recently!

F19 has a factor: 37590055514133754286524446080499713
Congrats to GIMPS and Buckle!
Quote:
Originally Posted by Prime95 View Post
Anyone want to test if this completes the factorization of F19?
I'll run the PRP real quick. Looks like it'll only take 10 minutes on one core of my semi-slow CPU.
Quote:
Originally Posted by mdettweiler View Post
Per factordb.com, a 15,770-digit composite cofactor remains.

Edit: Regarding the primality of the factor, that has also been automatically proven by the above-linked website upon submission of the factor.
The 35-digit factor is proven prime, the big cofactor is unknown, not PRP, yet. 50% using Prime95, this line: PRP=1,2,524288,1 umm...what happened to my known factors? I had put in the bit depth, tests saved, and known factors like whatsnew.txt says to and assumed that'd mean it'd run the PRP on the cofactor remaining after those factors. I guess I'll just wait and see what Prime95 PRPs...
Edit 2: Ah, I missed that the known factors had to be inside quotes. I put that in the other worker, and they both resumed from the save point of the first one. I suppose there's no reason that's wrong...anyway, both will finish soon (>75%)
Edit 3:
Code:
[Fri Jul 17 20:12:38 2009]
UID: tim_s/tim, F19 is not prime.  RES64: 449FBCA640B4FA27. Wd1: 75E095DF,00000000
UID: tim_s/tim, F19/known_factors is not prime.  RES64: 03B53E7A627BF963. Wd1: 75E095DF,00000000
Known factors used for PRP test were: 70525124609,646730219521,37590055514133754286524446080499713
(the second line is the only one you need to look at) Sorry, looks like we've got more work to do.

Last fiddled with by Mini-Geek on 2009-07-18 at 01:14
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Old 2009-07-18, 01:15   #5
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Quote:
Originally Posted by Mini-Geek View Post
The 35-digit factor is proven prime, the big cofactor is unknown, not PRP, yet. 50% using Prime95, this line: PRP=1,2,524288,1 umm...what happened to my known factors? I had put in the bit depth, tests saved, and known factors like whatsnew.txt says to and assumed that'd mean it'd run the PRP on the cofactor remaining after those factors. I guess I'll just wait and see what Prime95 PRPs...
Edit 2: Ah, I missed that the known factors had to be inside quotes. I put that in the other worker, and they both resumed from the save point of the first one. I suppose there's no reason that's wrong...anyway, both will finish soon (>75%)
This line:
Code:
PRP=1,2,524288,+1,"70525124609,646730219521,37590055514133754286524446080499713"
And I just got this:

Code:
[Work thread Jul 17 20:16] F19/known_factors is not prime.  RES64: C61CCF4C8ABEF914. Wd8: 75E095DF,00000000
[Work thread Jul 17 20:16] Known factors used for PRP test were: 70525124609,646730219521,37590055514133754286524446080499713
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Old 2009-07-18, 01:15   #6
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I ran it with

Code:
PRP=1,2,524288,1,"70525124609,646730219521,37590055514133754286524446080499713"
The result:
Code:
[Work thread Jul 18 03:29] F19/known_factors is not prime.  RES64: C61CCF4C8ABEF914. Wd8: 75E095DF,00000000
[Work thread Jul 18 03:29] Known factors used for PRP test were: 70525124609,646730219521,37590055514133754286524446080499713
Alex

Edit: Mini-Geek, your RES64 differs. I used mprime 25.11 64-bit.

Last fiddled with by akruppa on 2009-07-18 at 01:18 Reason: How's that for a fast double-check? :)
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Old 2009-07-18, 01:16   #7
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Hmm, my RES64 is different from yours (Mini-Geek).

EDIT: It matches akruppa's though.

Last fiddled with by jrk on 2009-07-18 at 01:16
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Old 2009-07-18, 01:22   #8
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Quote:
Originally Posted by Mini-Geek View Post
Edit 2: Ah, I missed that the known factors had to be inside quotes. I put that in the other worker, and they both resumed from the save point of the first one. I suppose there's no reason that's wrong...anyway, both will finish soon (>75%)
Edit 3:
Code:
[Fri Jul 17 20:12:38 2009]
UID: tim_s/tim, F19 is not prime.  RES64: 449FBCA640B4FA27. Wd1: 75E095DF,00000000
UID: tim_s/tim, F19/known_factors is not prime.  RES64: 03B53E7A627BF963. Wd1: 75E095DF,00000000
Known factors used for PRP test were: 70525124609,646730219521,37590055514133754286524446080499713
(the second line is the only one you need to look at) Sorry, looks like we've got more work to do.
You might have found a prime95 bug. You started a PRP without known factors, added the known factors and resumed and ended up with a different result than we did.
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Old 2009-07-18, 01:24   #9
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Prime95 version 25.11 64-bit

Code:
[Sat Jul 18 02:22:47 2009]
F19/known_factors is not prime.  RES64: C61CCF4C8ABEF914. Wd4: 75E095DF,00000000
Known factors used for PRP test were: 70525124609,646730219521,37590055514133754286524446080499713
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Old 2009-07-18, 01:25   #10
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I think it's quite safe to say my result was incorrect and akruppa's and jrk's were correct.
Now the question is why was mine incorrect. Are the save files between F19 and F19/known_factors incompatible? It was used automatically. If they're not compatible and that's the cause of the difference, George ought to fix that (I'm sure it rarely comes up, but it's a problem nonetheless). Perhaps mark the save files with a short hash of the known factors, if any? If they are supposed to be compatible, then there's a bug (we could run another test or two to double check, but it seems pretty clear to me) related to resuming from a save file of the no-known-factors version.
I used Prime95 25.11 build 2, 32-bit, on Windows XP, Athlon. I can post any log files that are wanted (and not auto-deleted already). I began the PRP of F19 on Worker #2, then stopped at about bit 330,000, added the F19/known_factors to Worker #1 (keeping F19 in #2) and restarted Prime95. They both resumed from the save file left by F19.

Last fiddled with by Mini-Geek on 2009-07-18 at 01:29
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Old 2009-07-18, 01:32   #11
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When I run the test with the new factor omitted, I get RES: AD48BE5F089980AC. Does not match Mini-Geek's, either. Strange.

Alex
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