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Old 2018-06-04, 07:30   #1
ICWiener
 
Jun 2018

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Default How does one prove that a mersenne prime found with CUDALucas is really prime?

Let me refine the question. For instance, the prime-testing 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?
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Old 2018-06-04, 08:10   #2
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Quote:
Originally Posted by ICWiener View Post
What stops someone from claiming "I just proved that M41033333333323 is prime using CUDALucas", and wasting everyone's time who tries to verify it?
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.
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Old 2018-06-04, 08:21   #3
ICWiener
 
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So using CUDALucas to prove the primality of a mersenne number is not very useful?
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Old 2018-06-04, 08:50   #4
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Quote:
Originally Posted by ICWiener View Post
So using CUDALucas to prove the primality of a mersenne number is not very useful?
The various proofs on different hardware and software are all useful!

Quote:
To be thorough, the prime number was independently verified with four different programs running on various hardware configurations.

Last fiddled with by paulunderwood on 2018-06-04 at 08:52
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Old 2018-06-04, 09:02   #5
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Quote:
Originally Posted by ICWiener View Post

What stops someone from claiming "I just proved that M41033333333323 is prime using CUDALucas", and wasting everyone's time who tries to verify it?
IIRC, CUDALucasa can't test Mersenne exponents that big. This could be a (negative) verification...
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Old 2018-06-04, 09:30   #6
ICWiener
 
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That was just a random prime number. Replace it with any number verifiable by CUDALucas.
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Old 2018-06-04, 13:09   #7
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An LL verification, even if it takes a significant amount of time, is still a very fast way to verify a Mersenne presumed-prime.

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 2018-06-04 at 13:10
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Old 2018-06-04, 13:12   #8
ICWiener
 
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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?
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Old 2018-06-04, 13:32   #9
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Quote:
Originally Posted by ICWiener View Post
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?
Yes, once.
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Old 2018-06-04, 13:57   #10
retina
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Quote:
Originally Posted by ICWiener View Post
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?
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 2018-06-04 at 13:58
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Old 2018-06-04, 14:14   #11
ICWiener
 
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Thank you all for your replies. This is exactly what I was looking for.
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