(257131 - 1)/61481396117165983261035042726614288722959856631

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:(257131 - 1)/61481396117165983261035042726614288722959856631
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c59 : Metcalfe, OpenPFGW, Primo
Decimal Digits:17152   (log10 is 17151.355938558)
Rank (*):73633 (digit rank is 1)
Entrance Rank (*):63078
Currently on list? (*):short
Submitted:12/16/2015 13:12:42 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:120768
Status Flags:Verify, TrialDiv
Score (*):34.1109 (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 103
Subcategory: "ECPP"
(archival tag id 218148, tag last modified 2023-03-11 16:02:30)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 12
Subcategory: "Mersenne cofactor"
(archival tag id 218149, tag last modified 2023-03-11 16:02:31)

User comments about this prime (disclaimer):

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David Metcalfe writes (16 Dec 2015):  (report abuse)

Certificate available from here.

PRP found by D.Broadhurst and W.Edgington, Sep 2009.

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^57131-1)/61481396117165983261035042726614288722959856631" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (2^57131-1)/6148139611...2959856631 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.19% proof) (2^57131-1)/6148139611...2959856631 is Fermat and Lucas PRP! (22.1880s+0.1431s) [Elapsed time: 23.00 seconds]
modified2020-07-07 22:30:17
created2015-12-16 13:21:01

Query times: 0.0003 seconds to select prime, 0.001 seconds to seek comments.
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