As I get older I notice 2 things starting to happen:
1. I repeat myself 2. I repeat myself 
[QUOTE=Dr Sardonicus;566442]"It's not nice to make people spray coffee all over their monitors."[/QUOTE]Aka CN>K
Or have you forgotten that too? 
[QUOTE=xilman;566457]Aka CN>K
Or have you forgotten that too?[/QUOTE] I have never seen that before. Therefore I have not forgotten it. 
The 350th fullyfactored or probablyfullyfactored Mersenne number with prime exponent
The 350th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [URL="https://www.mersenne.org/M1399"]M1399[/URL].
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. 
[QUOTE=Maciej Kmieciak;566781]The 350th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [URL="https://www.mersenne.org/M1399"]M1399[/URL].
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.[/QUOTE]FWIW, I ran PariGP's isprime() on this PRP308 with the following result: [code]? n=(2^13991)/28875361/4320651071020341609502042221583629017824960697/9729831901051958663829453004687723271026191923786080297556081; ? isprime(n) %2 = 1[/code] 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 BailliePSW pseudo primality test (see ispseudoprime), Selfridge "p − 1" test if x − 1 is smooth enough, and AdlemanPomeranceRumelyCohenLenstra (APRCL) for general x.[/quote] 
@James,
[URL="https://primes.utm.edu/primes/page.php?id=132049"]M82939 cofactor[/URL] is certified prime 
Congrats for this nice result!
[QUOTE=paulunderwood;572397]@James,
[URL="https://primes.utm.edu/primes/page.php?id=132049"]M82939 cofactor[/URL] is certified prime[/QUOTE] Many congrats, Paul! Jean P.S. : How did you do the PRP test before the certification using Primo ? 
Thanks, Jean.
I merely got the candidate from [url]www.mersenne.ca[/url]. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path. 
[QUOTE=paulunderwood;572410]Thanks, Jean.
I merely got the candidate from [url]www.mersenne.ca[/url]. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path.[/QUOTE] Thank you for this detail! Jean 
[QUOTE=paulunderwood;572397][URL="https://primes.utm.edu/primes/page.php?id=132049"]M82939 cofactor[/URL] is certified prime[/QUOTE]I have updated [url=https://www.mersenne.ca/prp.php?show=2&min_exponent=82000&max_exponent=83000#M82939]my PRP list[/url], thanks.

[QUOTE=Jean Penné;572405]
P.S. : How did you do the PRP test before the certification using Primo ?[/QUOTE] [QUOTE=paulunderwood;572410]Thanks, Jean. I merely got the candidate from [url]www.mersenne.ca[/url]. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path.[/QUOTE] We had already a Prpcf test on this: [url]https://www.mersenne.org/report_exponent/?exp_lo=82939&exp_hi=&full=1[/url] 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]. 
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