mersenneforum.org I think (wish) I find a new prime number record
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2020-05-23, 18:03   #12
Glenio

May 2020

5 Posts
Prime Number

Quote:
 Originally Posted by kriesel P-1 to full PrimeNet bounds on M102589933 under way here, will complete in hours. https://www.mersenne.ca/exponent/102589933 says 5.6% probability of factor, no p-1 result reported yet. It would be silly to have primality tested it without doing that first. Maybe he meant a Fermat number. That claim would be safe from computational attack for a while. As stated in his post, a large power of two being prime, it's too absurd a claim to even bother including in the count in the "dubious claims" list behind the stats in https://www.mersenneforum.org/showpo...04&postcount=5 There are few rhyming prime exponents surviving even cursory TF above M82589933. 102589933 NF 74, further TF assigned to gpu72, P-1 underway 112589933 small factor 222589933 small factor 232589933 NF 71, go to 79 assigned, no p-1 yet 2290000,68700000 312589933 small factors 532589933 smallish factor 612589933 smallish factor 642589933 NF 70, go to 84 assigned, no p-1 yet 5740000,172200000 652589933 NF 71, go to 84 assigned, no p-1 yet 5820000,174600000 672589933 smallish factors 702589933 small factors 892589933 smallish factor 912589933 smallish factor 952589933 small factors (up to 999M) The 3 other survivors are being addressed with TF and may get some P-1 attention after.
70237298350549551468899 á is congruent with 1 (mod 4) and no cofactor is also known; therefore, there may still be a chance that 2 ^ 70237298350549551468899-1 is prime. This is just an example that I am taking into account.

2020-05-23, 18:38   #13
paulunderwood

Sep 2002
Database er0rr

5·701 Posts

Quote:
 Originally Posted by Glenio 70237298350549551468899 á is congruent with 1 (mod 4) and no cofactor is also known; therefore, there may still be a chance that 2 ^ 70237298350549551468899-1 is prime. This is just an example that I am taking into account.
Is it 3 mod 4?

How many tons of coal are needed to LL test it?

What do you calculate the "chance" of being prime is?

Let me give you an example prime p=2^82589933-1 definitely has no small factors. So is 2^p-1 prime? Anyone?

Last fiddled with by paulunderwood on 2020-05-23 at 18:47

2020-05-23, 18:58   #14
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×4,591 Posts

Quote:
 Originally Posted by Glenio This is the number 2^102589933
.
Attached Thumbnails

2020-05-23, 21:26   #15
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

129B16 Posts

Quote:
 Originally Posted by Glenio 70237298350549551468899 á is congruent with 1 (mod 4) and no cofactor is also known; therefore, there may still be a chance that 2 ^ 70237298350549551468899-1 is prime. This is just an example that I am taking into account.
That reply to my post has nothing to do with my post. It's a ~75.89 bit exponent, making the corresponding Mersenne number untestable for primality or P-1 factoring in existing software, or realistic hardware lifetime or memory capacity, and is only factorable by slow cpu TF. But it earns a spot in the dubious-claims list, for which the track record is zero primes proven to date of several dozen entries; a handful yet to be resolved.

Last fiddled with by kriesel on 2020-05-23 at 21:27

 2020-05-23, 22:04 #16 kladner     "Kieren" Jul 2011 In My Own Galaxy! 2×5,059 Posts Wouldn't this be at home in: http://primes.utm.edu/notes/crackpot.html Miscellaneous Math?
2020-05-23, 23:25   #17
masser

Jul 2003

22·7·53 Posts

Quote:
 Originally Posted by kladner Wouldn't this be at home in: http://primes.utm.edu/notes/crackpot.html Miscellaneous Math?
seconded.

 2020-05-24, 19:52 #18 Kalli Hofmann     "Karl-Heinz Hofmann" Jan 2017 Gr.-Rohrheim Germany 2410 Posts What do you claim ? : Is 2 ^ 70237298350549551468899 – 1 a prime Number ? or is 2 ^ 102589933 – 1 a prime Number ? Please be accurate with your claims.
2020-05-25, 20:43   #19
Dylan14

"Dylan"
Mar 2017

13·41 Posts

Quote:
 Originally Posted by Kalli Hofmann What do you claim ? : Is 2 ^ 70237298350549551468899 – 1 a prime Number ? or is 2 ^ 102589933 – 1 a prime Number ? Please be accurate with your claims.
With the first number - I used factor5 to test factors up to 2^110. No factors found. This doesn't mean that it is prime, because in order to test that this number is prime, I would need the LL test, but this number is far beyond anyone's compute power. Not going to bother testing it farther...
With regards to the second - someone is running a PRP test on it. Assuming the machine that is running it is being run 24/7 on this number and it is a reasonably modern machine, we should know within a few weeks whether it is probably prime (in which case it will be tested with LL to conclude definitively whether it is prime) or not (in which case it's composite).

 2020-05-26, 11:18 #20 Kalli Hofmann     "Karl-Heinz Hofmann" Jan 2017 Gr.-Rohrheim Germany 23·3 Posts Going to 111,67 bit but still no factor. Going further a little bit.
 2020-05-30, 09:31 #21 Jan S   Oct 2018 Slovakia 1318 Posts M102589933 is(probably) not prime. I tested with GPUowl.
 2020-05-30, 13:59 #22 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 8,941 Posts Thanks, we can now leave this to rest in peace.

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