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 2021-10-24, 19:32 #1 piforbreakfast   Oct 2020 Terre Haute, IN 23·13 Posts DC has been completed but no factors found So does this mean this exponent is prime now that a double-check has found no factors, or is another test still pending? https://www.mersenne.ca/exponent/63459197 EDIT: Scratch that, does this mean then that a PRP is now needed to see if it's prime? Last fiddled with by piforbreakfast on 2021-10-24 at 19:34
2021-10-24, 19:59   #2
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

2×32×277 Posts

Quote:
 Originally Posted by piforbreakfast So does this mean this exponent is prime now that a double-check has found no factors, or is another test still pending? https://www.mersenne.ca/exponent/63459197 EDIT: Scratch that, does this mean then that a PRP is now needed to see if it's prime?
Successfully Double Checked means it is verified NOT prime.
PRP is not necessary.
PRP/Cert is a recent replacement for the LL/DC tests.

A separate process can try to find factors (TF or P1 or ECM).
However, is the factors are large enough they will not be found by these methods...in the foreseen future anyway.

2021-10-24, 20:46   #3
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

17D816 Posts

Quote:
 Originally Posted by piforbreakfast So does this mean this exponent is prime now that a double-check has found no factors, or is another test still pending? https://www.mersenne.ca/exponent/63459197 EDIT: Scratch that, does this mean then that a PRP is now needed to see if it's prime?
1. All the exponents considered are prime. For the corresponding mersenne number to have ANY chance of being prime, the exponent must be prime. https://www.mersenneforum.org/showpo...13&postcount=4
2. Primality tests, whether first test, double checks, triple checks, whether by LL, or by PRP of various types, do not produce factors. Standard TF or P-1 factoring or other factoring methods (P+1, ECM, rarely applied to wavefront candidates) may produce specific factors.
3. Lucas-Lehmer test and PRP are distinct types of tests for primality. LL is conclusive if performed correctly. PRP returning a composite result is conclusive if performed correctly.
4. Any one of the following is considered sufficient to eliminate a Mersenne number as a possible prime:
1. a composite exponent
2. a factor found
3. two or more matching LL final residues >0 indicating composite, and if systematic error is ruled out, such as matching bad 0x02 residues in some previous versions of CUDALucas, CLLucas etc. (typ effort ~2.04 LL ~2.04 PRP; higher relative effort at higher exponent due to increasing error rate with run time)
4. two or more matching PRP final residues of the same PRP type (typ effort ~2.006 PRP) indicating composite
5. PRP/GEC/proof generation followed by successful certification (typ effort ~1.005 PRP) indicating composite
5. PRP can prove a Mersenne number composite. It does not quite prove a prime prime. It yields "proven composite" or "probably prime".
6. Any PRP test yielding "probably prime" will be considered the discovery of a new Mersenne prime, IF multiple LL tests following on different software and hardware confirm the Mersenne number is prime. Despite >120K verified PRP tests, that has not yet happened.

Last fiddled with by kriesel on 2021-10-24 at 21:43

2021-10-25, 05:51   #4
piforbreakfast

Oct 2020
Terre Haute, IN

23·13 Posts

Quote:
 Originally Posted by kriesel Your post seems to indicate a lack of understanding of multiple fundamentals. Please read https://www.mersenneforum.org/showth...665#post521665 [LIST=1][*] All the exponents considered are prime. For the corresponding mersenne number to have ANY chance of being prime, the exponent must be prime. https://www.mersenneforum.org/showpo...13&postcount=4
You said what I meant to say. I realize all exponents must be prime, it just didn't come out that way. I appreciate the primer on primality testing and elimination.

2021-10-26, 01:40   #5
tuckerkao

"Tucker Kao"
Jan 2020

25×3×7 Posts

Quote:
 Originally Posted by kriesel 6. Any PRP test yielding "probably prime" will be considered the discovery of a new Mersenne prime, IF multiple LL tests following on different software and hardware confirm the Mersenne number is prime. Despite >120K verified PRP tests, that has not yet happened.[/INDENT]
If someone runs the PRP on M82,589,933, what will the result line be looking like?

2021-10-26, 01:59   #6
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

22·2,467 Posts

Quote:
 Originally Posted by tuckerkao If someone runs the PRP on M82,589,933, what will the result line be looking like?
You can try by yourself and see. Pick a smaller exponent, like M47 or M48 or so, so you won't waste much time.

2021-10-26, 02:03   #7
tuckerkao

"Tucker Kao"
Jan 2020

25·3·7 Posts

Quote:
 Originally Posted by LaurV You can try by yourself and see. Pick a smaller exponent, like M47 or M48 or so, so you won't waste much time.
The problem is that when I finish the PRP, Prime95 will upload my result to the server and add in an unnecessary result entry. I definitely don't want a PRP cert from another user too when a Mersenne number was already a proven prime.

Users can even run the PRP on an exponent with a known factor and Prime95 won't recognize it.

Last fiddled with by tuckerkao on 2021-10-26 at 02:35

 2021-10-26, 02:39 #8 slandrum   Jan 2021 California 4578 Posts So don't submit the result - nothing says you have to.
2021-10-26, 05:25   #9
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

23·7·109 Posts

Quote:
 Originally Posted by LaurV You can try by yourself and see.
Depends on the app and PRP type, but:
Code:
{"exponent":"82589933", "worktype":"PRP-3", "status":"P", "program":{"name":"gpuowl", "version":"5.0-9c13870"}, "timestamp":"2018-12-26 20:15:41 UTC", "aid":"0", "fft-length":4718592, "res64":"fffffffffffffffc", "residue-type":4}
All known Mersenne primes practical have already long ago had confirming PRP/GEC runs as a reliability test of Gpuowl.
https://www.mersenneforum.org/showpo...1&postcount=13
https://www.mersenneforum.org/showpo...83&postcount=8

 2021-10-26, 05:40 #10 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 22·2,467 Posts Grrr...

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