20180604, 07:30  #1 
Jun 2018
11_{16} Posts 
How does one prove that a mersenne prime found with CUDALucas is really prime?
Let me refine the question. For instance, the primetesting software Primo generates a "prime certificate" file that can be shared easily in order to prove that a given prime has been deterministically verified as prime. CUDALucas does not provide such a file. Instead, it writes a "result.txt" which simply confirms that the given mersenne number is indeed prime, without "proof".
What stops someone from claiming "I just proved that M41033333333323 is prime using CUDALucas", and wasting everyone's time who tries to verify it? 
20180604, 08:10  #2 
Jun 2003
3·11·149 Posts 
We can ask them to produce the last checkpoint file written by CudaLucas and then run the rest of the LL test from there. Other than that, no shortcut verification is known.

20180604, 08:21  #3 
Jun 2018
17 Posts 
So using CUDALucas to prove the primality of a mersenne number is not very useful?

20180604, 08:50  #4  
Sep 2002
Database er0rr
2^{2}×5×181 Posts 
Quote:
Quote:
Last fiddled with by paulunderwood on 20180604 at 08:52 

20180604, 09:02  #5 
Banned
"Luigi"
Aug 2002
Team Italia
2^{2}×3×401 Posts 

20180604, 09:30  #6 
Jun 2018
17 Posts 
That was just a random prime number. Replace it with any number verifiable by CUDALucas.

20180604, 13:09  #7 
"Mihai Preda"
Apr 2015
2×677 Posts 
An LL verification, even if it takes a significant amount of time, is still a very fast way to verify a Mersenne presumedprime.
For comparison, there are hundreds of LL done daily just to verify that X is indeed not prime (I'm referring to double checks, done after an initial LL turned up negative). Last fiddled with by preda on 20180604 at 13:10 
20180604, 13:12  #8 
Jun 2018
21_{8} Posts 
So if one came forward with the claim that "I found M*** a new Mersenne prime using CUDALucas, and I have nothing but the last checkpoint file to prove it", would be taken seriously?

20180604, 13:32  #9 
"Mihai Preda"
Apr 2015
2·677 Posts 

20180604, 13:57  #10 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{3}·3^{2}·5·17 Posts 
It isn't just CUDALucas, but all LL test programs that have the same "flaw". Since there is currently no known fast verification method, we are left with asking the claimant to produce the penultimate checkpoint file. So if you can produce a checkpoint file and someone else runs the last few iterations and gets the same result then you will be famous. But if instead it is bogus then you may have trouble with people believing you in the future. Either your machine/GPU is faulty, or something more sinister is going on.
Last fiddled with by retina on 20180604 at 13:58 
20180604, 14:14  #11 
Jun 2018
17 Posts 
Thank you all for your replies. This is exactly what I was looking for.

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