20201217, 17:02  #540 
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 
20201217, 17:40  #541 
Bamboozled!
"đ’‰ºđ’ŒŒđ’‡·đ’†·đ’€"
May 2003
Down not across
10646_{10} Posts 

20201217, 21:25  #542 
Feb 2017
Nowhere
10564_{8} Posts 

20201220, 18:15  #543 
Nov 2018
Poland
3×5 Posts 
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 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. 
20201220, 19:48  #544  
Feb 2017
Nowhere
2^{2}×1,117 Posts 
Quote:
Code:
? n=(2^13991)/28875361/4320651071020341609502042221583629017824960697/9729831901051958663829453004687723271026191923786080297556081; ? isprime(n) %2 = 1 The manual entry says Quote:
Last fiddled with by Dr Sardonicus on 20201221 at 21:03 Reason: Add code tags 

20210224, 06:42  #545 
Sep 2002
Database er0rr
2^{2}×5×181 Posts 

20210224, 09:16  #546  
May 2004
FRANCE
1000111111_{2} Posts 
Congrats for this nice result!
Quote:
Jean P.S. : How did you do the PRP test before the certification using Primo ? 

20210224, 09:46  #547 
Sep 2002
Database er0rr
2^{2}×5×181 Posts 
Thanks, Jean.
I merely got the candidate from www.mersenne.ca. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas Ă la BPSW before embarking on a lengthy ECPP path. 
20210224, 09:51  #548  
May 2004
FRANCE
23F_{16} Posts 
Quote:
Jean 

20210224, 14:46  #549  
"James Heinrich"
May 2004
exNorthern Ontario
2·1,663 Posts 
Quote:


20210224, 20:17  #550  
"Robert Gerbicz"
Oct 2005
Hungary
10110110010_{2} Posts 
Quote:
Quote:
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 20210224 at 20:18 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Smallest exponent for mersenne notfactored  preda  PrimeNet  10  20181104 00:47 
Largest Mersenne Number Fully Factored?  c10ck3r  Data  49  20171210 19:39 
Possibility of a FullyFactored Number  Trejack  FactorDB  7  20160514 05:38 
Estimating the number of primes in a partiallyfactored number  CRGreathouse  Probability & Probabilistic Number Theory  15  20140813 18:46 
Number of distinct prime factors of a Double Mersenne number  aketilander  Operazione Doppi Mersennes  1  20121109 21:16 