20110301, 15:59  #1 
Feb 2010
Sweden
173_{10} Posts 
Is there independent check for found factors?
Out of curiosity I wonder if there is an Prime95 independent check that a factor is actually dividing an exponent? I guess the server checks somehow that the factor is not a mistake.

20110301, 17:00  #2  
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{2}×7×359 Posts 
Quote:
Factor found reports to the PrimeNet server are impossible to fake. (There is a corollary to this, which I won't go into....) 

20110304, 12:27  #3 
Feb 2010
Sweden
173 Posts 
Thanks for the answer. I was more curious if it is Prime95 independent, but probably the division is trivial once you know a factor. I am not saying anything about the program, I simply like independent verifications.

20110304, 17:57  #4 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
23613_{8} Posts 
The factors are stored in the database. They are publicly available. A person could write some code that fetches the exponent and factor, then checks them. My understanding is that the total time for a single PC to verify each factor for the entire database would be less than 2 months (wild guess).

20110304, 21:48  #5 
A Sunny Moo
Aug 2007
USA (GMT5)
3×2,083 Posts 
PrimeNet's check is Prime95 independent; since the division is trivial, it is probably just done as a little bit of serverside PHP or ASP code in the routines that handle client communication. There is also an additional check, performed with the msieve factoring program (of no relation to Prime95) to verify that the factor reported is PRP (probably prime); if it is composite, then msieve will split it into its constituent prime factors within a minute or two. (The cofactor of the entire Mersenne number is not checked for primality because it is extremely large and this would be very timeconsuming, but that's fine since as long as the factor divides the Mersenne number, it is proven composite regardless of the cofactor's primality.)
Last fiddled with by mdettweiler on 20110304 at 21:49 
20110304, 23:51  #6  
"Oliver"
Mar 2005
Germany
11×101 Posts 
Quote:
Code:
o@Lysithea:~/mfaktc/defactor> time ./defactor.exe 13828261 1979553586274192263311048622055057969 The factor 1979553586274192263311048622055057969 divides 2^13828261 1! K = 71576374870064726985954655544 The factor 1979553586274192263311048622055057969 is probably prime real 0m0.001s user 0m0.000s sys 0m0.000s Oliver 

20110305, 00:20  #7 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10123_{10} Posts 

20110310, 14:55  #8 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3×1,619 Posts 
However, what won't be verified is NO FACTOR found results.
If due to an error the software mistakenly misses a factor, the only way to verify it would be to rerun the TF....which is NOT done today unless someone chooses to do so manually or via a different program. This simply means the exponent will (unnecessarily) continue to be available to further TF / P1 / LL / DC. That was a thread a couple years ago that discussed a known bug in the factoring code in an old version but it suggests that the suspect ranges were all rerun. 
20110310, 22:19  #9  
"Richard B. Woods"
Aug 2002
Wisconsin USA
7692_{10} Posts 
Yes, it's well known that, in general, proving a negative is difficult. :)
Quote:
See the neighboring thread "M2629093 has a factor: 63721413359381377" at http://mersenneforum.org/showthread.php?t=15318 for more discussion of the missedfactors issue. Note George's comment in post #22 and mine in post #24 about the relative merits of devoting resources to reTFing past searches (i.e., perfectionism) versus going a bit level deeper (i.e., productivity). ReTFing all past searches would take the same amount of work as simply extending all previous TF by one more bit, but would be less productive. ReTFing may find a few missed factors, but extending all past TF by one bit would find hundreds of factors. Neither would help GIMPS's throughput. Last fiddled with by cheesehead on 20110310 at 22:28 

20110311, 17:03  #10  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
11371_{8} Posts 
Quote:
http://www.youtube.com/watch?v=sh163...eature=related http://www.youtube.com/watch?v=KiIP_KDQmXs 

20110312, 18:51  #11 
"GIMFS"
Sep 2002
Oeiras, Portugal
2751_{8} Posts 

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