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 2020-12-17, 17:02 #540 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 43·107 Posts As I get older I notice 2 things starting to happen: 1. I repeat myself 2. I repeat myself
2020-12-17, 17:40   #541
xilman
Bamboozled!

"đ’‰ºđ’ŒŒđ’‡·đ’†·đ’€­"
May 2003
Down not across

246268 Posts

Quote:
 Originally Posted by Dr Sardonicus "It's not nice to make people spray coffee all over their monitors."
Aka C|N>K

Or have you forgotten that too?

2020-12-17, 21:25   #542
Dr Sardonicus

Feb 2017
Nowhere

2×7×11×29 Posts

Quote:
 Originally Posted by xilman Aka C|N>K Or have you forgotten that too?
I have never seen that before. Therefore I have not forgotten it.

 2020-12-20, 18:15 #543 Maciej Kmieciak   Nov 2018 Poland 3×5 Posts The 350th fully-factored or probably-fully-factored Mersenne number with prime exponent The 350th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M1399. The most recent factor (61 digits) was found by Ryan Propper on December 19 (UTC) and the PRP test was done by mikr and myself. There are 3 factors in all, plus the cofactor.
2020-12-20, 19:48   #544
Dr Sardonicus

Feb 2017
Nowhere

105628 Posts

Quote:
 Originally Posted by Maciej Kmieciak The 350th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M1399. The most recent factor (61 digits) was found by Ryan Propper on December 19 (UTC) and the PRP test was done by mikr and myself. There are 3 factors in all, plus the cofactor.
FWIW, I ran Pari-GP's isprime() on this PRP308 with the following result:

Code:
? n=(2^1399-1)/28875361/4320651071020341609502042221583629017824960697/9729831901051958663829453004687723271026191923786080297556081;

? isprime(n)

%2 = 1
It didn't take very long.

The manual entry says
Quote:
 3.4.31 isprime(x, {flag = 0}): true (1) if x is a (proven) prime number, false (0) otherwise. This can be very slow when x is indeed prime and has more than 1000 digits, say. Use ispseudoprime to quickly check for pseudo primality. See also factor. If flag = 0, use a combination of Baillie-PSW pseudo primality test (see ispseudoprime), Selfridge "p âˆ’ 1" test if x âˆ’ 1 is smooth enough, and Adleman-Pomerance-Rumely-Cohen-Lenstra (APRCL) for general x.

Last fiddled with by Dr Sardonicus on 2020-12-21 at 21:03 Reason: Add code tags

 2021-02-24, 06:42 #545 paulunderwood     Sep 2002 Database er0rr 2·33·67 Posts @James, M82939 cofactor is certified prime
2021-02-24, 09:16   #546
Jean PennĂ©

May 2004
FRANCE

52·23 Posts
Congrats for this nice result!

Quote:
 Originally Posted by paulunderwood @James, M82939 cofactor is certified prime
Many congrats, Paul!

Jean

P.S. : How did you do the PRP test before the certification using Primo ?

 2021-02-24, 09:46 #547 paulunderwood     Sep 2002 Database er0rr E2216 Posts Thanks, Jean. I merely got the candidate from www.mersenne.ca. I might have run a 3-PRP to be sure-ish. Anyway, Primo does a quick Fermat+Lucas Ă  la BPSW before embarking on a lengthy ECPP path.
2021-02-24, 09:51   #548
Jean PennĂ©

May 2004
FRANCE

57510 Posts

Quote:
 Originally Posted by paulunderwood Thanks, Jean. I merely got the candidate from www.mersenne.ca. I might have run a 3-PRP to be sure-ish. Anyway, Primo does a quick Fermat+Lucas Ă  la BPSW before embarking on a lengthy ECPP path.
Thank you for this detail!

Jean

2021-02-24, 14:46   #549
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

2·1,663 Posts

Quote:
 Originally Posted by paulunderwood M82939 cofactor is certified prime
I have updated my PRP list, thanks.

2021-02-24, 20:17   #550
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

145810 Posts

Quote:
 Originally Posted by Jean PennĂ© P.S. : How did you do the PRP test before the certification using Primo ?
Quote:
 Originally Posted by paulunderwood Thanks, Jean. I merely got the candidate from www.mersenne.ca. I might have run a 3-PRP to be sure-ish. Anyway, Primo does a quick Fermat+Lucas Ă  la BPSW before embarking on a lengthy ECPP path.
We had already a Prp-cf test on this:
https://www.mersenne.org/report_expo...exp_hi=&full=1

Notice that for N=(k*2^n+c)/d we're using a Fermat test using
base^d as base, then
(base^d)^N=base^d mod N should hold for a prp number. So

base^(k*2^n+c)==base^d mod N, to help a lot we're using reduction mod (d*N)=mod (k*2^n+c).
Then do only one big division at the end of the test, in real life d is "small", at most ~1000 bits. And you can build in a strong check in the routine like for the normal prp test for k*2^n+c numbers. There is only a very small slow down at error check, because here our base is "large".

ps. so actually p95 has done a Fermat test using 3^d as base, and not 3. The reason is that we have a check only for 3^d [or base^d].

Last fiddled with by R. Gerbicz on 2021-02-24 at 20:18

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