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Old 2018-06-17, 11:58   #1
ICWiener
 
Jun 2018

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Default In CUDALucas, do I have to wait until 100% completion before knwoing that my cadidate is composite?

I am running a CUDALucas Mersenne prime test since several months, and I am reaching the 20% mark. My candidate is purely random[1] (the prime exponent, that is), so I do not expect to find a new Mersenne prime. However, the fact that CUDALucas continues to compute for months without ruling out that it's composite makes me wonder:

- does CUDALucas need to reach 100% before giving a "verdict"?
- should I entertain hopes that finding a prime has more probability, now that several months of computing have elapsed?
_________________________

[1] i.e., it doesn't fulfill any of the criteria of the new Mersenne conjecture.
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Old 2018-06-17, 12:08   #2
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Quote:
Originally Posted by ICWiener View Post
I am running a CUDALucas Mersenne prime test since several months, and I am reaching the 20% mark. My candidate is purely random[1] (the prime exponent, that is), so I do not expect to find a new Mersenne prime. However, the fact that CUDALucas continues to compute for months without ruling out that it's composite makes me wonder:

- does CUDALucas need to reach 100% before giving a "verdict"?
- should I entertain hopes that finding a prime has more probability, now that several months of computing have elapsed?
_________________________

[1] i.e., it doesn't fulfill any of the criteria of the new Mersenne conjecture.
A Lucas Lehmer primality test needs to complete to tell if a Mersenne number is prime or not. edit: or if p and 2p+1 are both 3 mod 4 and prime we know it's composite but only a few cases like that.

Last fiddled with by science_man_88 on 2018-06-17 at 12:35
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Old 2018-06-17, 13:52   #3
ATH
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What graphic card are you running this on? How big is the exponent approximately?

It is not supposed to take many months, so either it is a very old card and/or you have chosen a way too large exponent.

It might also be one of those graphic cards that is best used for trial factoring because double precision speed (needed for LL test) is 32 times slower than single precision speed (used for trial factoring).
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Old 2018-06-17, 14:00   #4
ICWiener
 
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Quote:
Originally Posted by ATH View Post
What graphic card are you running this on? How big is the exponent approximately?

It is not supposed to take many months, so either it is a very old card and/or you have chosen a way too large exponent.

It might also be one of those graphic cards that is best used for trial factoring because double precision speed (needed for LL test) is 32 times slower than single precision speed (used for trial factoring).
I have chosen a very large exponent. The calculation's ETA is almost 300 days.
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Old 2018-06-17, 15:25   #5
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Only the final result matters, and it is a yes-or-no result.

Zero means yes it's prime, and non-zero means no it's not prime.

Any interim result (or the exact numerical value of a non-zero final result) is useful only for comparison purposes when it comes time for someone else to do a verification run, to double-check the accuracy of your test. If the two runs don't match then one or possibly both of them is wrong and further tests are needed.
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Old 2018-06-17, 15:36   #6
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Quote:
Originally Posted by ICWiener View Post
I have chosen a very large exponent. The calculation's ETA is almost 300 days.
Is the exponent in the 25.92 billion range ?

Last fiddled with by science_man_88 on 2018-06-17 at 15:36
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Old 2018-06-17, 16:39   #7
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Quote:
Originally Posted by science_man_88 View Post
Is the exponent in the 25.92 billion range ?
No. Max CUDALucas fft length is 64M & theoretically limited to 1143M. In practice it appears to be lower.
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Old 2018-06-17, 16:55   #8
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Originally Posted by kriesel View Post
No. Max CUDALucas fft length is 64M & theoretically limited to 1143M. In practice it appears to be lower.
Means either iteration times are above 22.7 ms per iteration or the computer isn't 24/7
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Old 2018-06-17, 17:29   #9
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Quote:
Originally Posted by science_man_88 View Post
Means either iteration times are above 22.7 ms per iteration or the computer isn't 24/7
Iteration times are around 60 ms, and the PC is on 24/7. Note that I'm only using a home PC, nothing fancy with a GeForce GTX Ti 1050. My exponent isn't in't the billions range, as someone suggested. Instead, it's in the 100 million.
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Old 2018-06-17, 18:45   #10
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Quote:
Originally Posted by ICWiener View Post
I am running a CUDALucas Mersenne prime test since several months, and I am reaching the 20% mark. My candidate is purely random[1] (the prime exponent, that is), so I do not expect to find a new Mersenne prime. However, the fact that CUDALucas continues to compute for months without ruling out that it's composite makes me wonder:

a- does CUDALucas need to reach 100% before giving a "verdict"?
b- should I entertain hopes that finding a prime has more probability, now that several months of computing have elapsed?
_________________________

[1] i.e., it doesn't fulfill any of the criteria of the new Mersenne conjecture.
Welcome to the hunt. (Futurama fan?)

a) yes
b) only in the sense that it has not obviously crashed yet. Only the last Lucas-Lehmer sequence output tells of primality status, the other iterations are necessary steps to reach it.

Did you use good practice, fft benchmarking the card, in CUDALucas for the fft lengths of interest, threads benchmarking the card, run the residue selftest, run memory test over the whole card, run a couple of low double checks to verify it's working at differing fft lengths, before tackling a several months or some years' length assignment? Check out the exponent? Confirm that 64-bit residues are changing from one status line to the next, and known-bad behavior not happening? What version CUDALucas is running? (V2.06 May 5 2017 beta?)
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Old 2018-06-17, 18:46   #11
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Quote:
Originally Posted by science_man_88 View Post
Means either iteration times are above 22.7 ms per iteration or the computer isn't 24/7
CUDALucas won't run 25 billion or even 2 billion exponent; 1.143 billion max exponent, for 64M fft length max.

Last fiddled with by kriesel on 2018-06-17 at 18:50
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