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Old 2020-04-09, 09:31   #1
jas
 
"Simon Josefsson"
Jan 2020
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Default How to request smallest >100M numbers for PRP?

I want to do PRP-testing of the smallest available first-time >100M numbers. I have enabled the "get the smallest exponents" setting. However, when I configure my client for SrvrPO1=153, I received large >100M numbers such as M332380313. While fun to work on such a large number, I would prefer to work on the minimal >100M numbers. Is this possible? Or do I have to do manual assignment (which I've never tried before)?


Thanks,
Simon
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Old 2020-04-09, 11:07   #2
S485122
 
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"Jacob"
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The smallest Mersenne number with one hundred million digits (100M) is 2332 192 810-1 and obviously not a prime.
I think you confuse the exponent with the resulting number.
2100 000 000-1 has "only" thirty million, one hundred and three thousand digits (30 103 000).

Jacob
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Old 2020-04-09, 11:11   #3
jas
 
"Simon Josefsson"
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Quote:
Originally Posted by S485122 View Post
The smallest Mersenne number with one hundred million digits (100M) is 2332 192 810-1 and obviously not a prime.
I think you confuse the exponent with the resulting number.
2100 000 000-1 has "only" thirty million, one hundred and three thousand digits (30 103 000).

Jacob

Thank you -- my mistake.



/Simon
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Old 2020-04-09, 14:03   #4
Uncwilly
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There many of the lowest 100M digit numbers that have a known factor. Of those that don't, many have had a first time check PRP or LL. And then a bunch of the remaining are already assigned to people. When you tell Prime95 that you want to do PRP on numbers that large, PrimeNet will normally assign you the lowest available number.
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Old 2020-05-04, 03:28   #5
Runtime Error
 
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I noticed a recent 100M digit PRP result (332356909) on the recently cleared list that a user presumably got through PrimeNet. It has only been TF'd to 77 bits and P-1 factoring hasn't been done, but a user spent nearly 5,000 GhZ/days doing PRP.

Most of these low 100M digit exponents haven't had much of the early work done on them that helps weed out composite numbers. If you have access to a graphics card, you'll usually want to Trial Factor (TF) them to 80+ bits. Additionally, you'll want to perform P-1 factoring before committing to a PRP. Good luck!

Last fiddled with by Runtime Error on 2020-05-04 at 03:31 Reason: spelling
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Old 2020-05-04, 15:51   #6
kriesel
 
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Quote:
Originally Posted by Runtime Error View Post
I noticed a recent 100M digit PRP result (332356909) on the recently cleared list that a user presumably got through PrimeNet. It has only been TF'd to 77 bits and P-1 factoring hasn't been done, but a user spent nearly 5,000 Ghz-days doing PRP.

Most of these low 100M digit exponents haven't had much of the early work done on them that helps weed out composite numbers. If you have access to a graphics card, you'll usually want to Trial Factor (TF) them to 80+ bits. Additionally, you'll want to perform P-1 factoring before committing to a PRP. Good luck!
Queued for TF to 81 on an RTX 2080 Super. Might save a someday DC.
https://www.mersenne.ca/exponent/332356909 says 1381 GhzDays for TF 77 to 81 bits. These are the cheap and plentiful Int32 TF GhzD (3072 GhzD/day on that gpu; 2.43% chance of factor found, or 5.4%/day for 0.45 days.)

P-1 says 172 GhzD, 5.59% chance of factor found to PrimeNet bounds, and those are the costly and less plentiful DPfloat kind. (~74GhD/day on an RTX 2080 Super gpu, or 2.4%/day for 2.3 days; I would actually use an AMD or low SP/DP ratio NVIDIA gpu or cpu instead. A Radeon VII could do it quickly, about 172/274 = .0.63 days)
The PRP test recently reported is by xebecer, and is sort of special in that it is a type 4 residue and zero offset. That indicates it was performed using gpuowl between about V4.3 and V6.5-30c0508 which marked the return to type 1 PRP residues. It would require prime95 or mprime with residue type 4 specified for a PRP DC. The use of older versions of gpuowl that produce type 4 residues is discouraged, because
  1. Double checks require extra care to make sure the matching nonstandard residue type 4 is performed again.
  2. Type-4-residue-capable versions of gpuowl are older and slower than current versions that do type 1.
  3. Gpuowl should not be used to double check gpuowl PRP tests, because both runs will be performed with zero shift.
  4. Type 1 PRP is the default for prime95 and mprime and I think other programs.
  5. Type 4 PRP may not be supported in other programs, such as mlucas.

Last fiddled with by kriesel on 2020-05-04 at 16:22
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Old 2020-05-06, 14:13   #7
kriesel
 
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Quote:
Originally Posted by Runtime Error View Post
I noticed a recent 100M digit PRP result (332356909) on the recently cleared list that a user presumably got through PrimeNet. It has only been TF'd to 77 bits and P-1 factoring hasn't been done, but a user spent nearly 5,000 GhZ/days doing PRP.

Most of these low 100M digit exponents haven't had much of the early work done on them that helps weed out composite numbers. If you have access to a graphics card, you'll usually want to Trial Factor (TF) them to 80+ bits. Additionally, you'll want to perform P-1 factoring before committing to a PRP. Good luck!
That one definitely should have been trial factored to the recommended gpu level. I found a factor.
In selecting single-primality-tested exponents to LL DC or PRP DC in the range from current wavefront up to 200M exponent, I'm finding that many of those also lack sufficient TF or P-1 or both.

Last fiddled with by kriesel on 2020-05-06 at 14:36
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Old 2020-05-08, 01:33   #8
Runtime Error
 
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Quote:
Originally Posted by kriesel View Post
That one definitely should have been trial factored to the recommended gpu level. I found a factor.
Ouch! At least you saved a DC though... congrats on the factor.

Last fiddled with by Runtime Error on 2020-05-08 at 01:47
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