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Old 2020-12-17, 17:02   #540
petrw1
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As I get older I notice 2 things starting to happen:

1. I repeat myself
2. I repeat myself
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Old 2020-12-17, 17:40   #541
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Quote:
Originally Posted by Dr Sardonicus View Post
"It's not nice to make people spray coffee all over their monitors."
Aka C|N>K


Or have you forgotten that too?
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Old 2020-12-17, 21:25   #542
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Quote:
Originally Posted by xilman View Post
Aka C|N>K


Or have you forgotten that too?
I have never seen that before. Therefore I have not forgotten it.
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Old 2020-12-20, 18:15   #543
Maciej Kmieciak
 
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Default 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.
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Old 2020-12-20, 19:48   #544
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Quote:
Originally Posted by Maciej Kmieciak View Post
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 − 1" test if x − 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
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Old 2021-02-24, 06:42   #545
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@James,

M82939 cofactor is certified prime
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Old 2021-02-24, 09:16   #546
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Default Congrats for this nice result!

Quote:
Originally Posted by paulunderwood View Post
@James,

M82939 cofactor is certified prime
Many congrats, Paul!

Jean

P.S. : How did you do the PRP test before the certification using Primo ?
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Old 2021-02-24, 09:46   #547
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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.
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Old 2021-02-24, 09:51   #548
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Quote:
Originally Posted by paulunderwood View Post
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
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Old 2021-02-24, 14:46   #549
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Quote:
Originally Posted by paulunderwood View Post
M82939 cofactor is certified prime
I have updated my PRP list, thanks.
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Old 2021-02-24, 20:17   #550
R. Gerbicz
 
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Quote:
Originally Posted by Jean Penné View Post
P.S. : How did you do the PRP test before the certification using Primo ?
Quote:
Originally Posted by paulunderwood View Post
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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