(228771 - 1)/104726441

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:(228771 - 1)/104726441
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c56 : Soule, Minovic, OpenPFGW, Primo
Decimal Digits:8653   (log10 is 8652.9139489036)
Rank (*):82031 (digit rank is 1)
Entrance Rank (*):58036
Currently on list? (*):no
Submitted:2/7/2012 04:58:18 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:104244
Status Flags:Verify
Score (*):31.9915 (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 337
Subcategory: "ECPP"
(archival tag id 213861, tag last modified 2023-03-11 16:02:30)
Mersenne cofactor (archivable *)
Prime on list: no, rank 22
Subcategory: "Mersenne cofactor"
(archival tag id 213862, tag last modified 2023-03-11 16:02:31)

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.

Predrag Minovic writes (11 Sep 2014):  (report abuse)
The certificate can be found here.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"(2^28771-1)/104726441" 2>&1 PFGW Version [GWNUM 26.5] (2^28771-1)/104726441 1/1 mro=0 trial factoring to 2457184 (2^28771-1)/104726441 has no small factor. [Elapsed time: 1.951 seconds]
modified2020-07-07 22:30:29
created2012-02-07 05:05:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"(2^28771-1)/104726441" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (2^28771-1)/104726441 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N+1 BLS with factored part 0.18% and helper 0.13% (0.68% proof) (2^28771-1)/104726441 is Fermat and Lucas PRP! (29.6894s+0.0003s) [Elapsed time: 30.00 seconds]
modified2020-07-07 22:30:29
created2012-02-07 05:08:01

Query times: 0.0003 seconds to select prime, 0.0006 seconds to seek comments.
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