(228759 - 1)/226160777

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:(228759 - 1)/226160777
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c60 : Lemsafer, Primo
Decimal Digits:8649   (log10 is 8648.9672280129)
Rank (*):80781 (digit rank is 1)
Entrance Rank (*):62604
Currently on list? (*):no
Submitted:9/24/2012 10:40:16 CDT
Last modified:9/24/2012 11:20:28 CDT
Database id:109394
Status Flags:Verify
Score (*):31.9901 (normalized score 0)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 331
Subcategory: "ECPP"
(archival tag id 214529, tag last modified 2022-11-14 11:36:29)
Mersenne cofactor (archivable *)
Prime on list: no, rank 21
Subcategory: "Mersenne cofactor"
(archival tag id 214530, tag last modified 2022-11-14 11:36:30)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014):  (report abuse)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"(2^28759-1)/226160777" 2>&1 PFGW Version [GWNUM 26.5] (2^28759-1)/226160777 1/1 mro=0 trial factoring to 2455982 (2^28759-1)/226160777 has no small factor. [Elapsed time: 1.976 seconds]
modified2020-07-07 17:30:24
created2012-09-24 10:48:01

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -tc -q"(2^28759-1)/226160777" 2>&1 PFGW Version [GWNUM 25.14] Primality testing (2^28759-1)/226160777 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N+1 BLS with factored part 0.09% and helper 0.08% (0.37% proof) (2^28759-1)/226160777 is Fermat and Lucas PRP! (23.8864s+0.0265s) [Elapsed time: 24.00 seconds]
modified2020-07-07 17:30:24
created2012-09-24 10:52:49

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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