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:

Verification status (*):PRP
Official Comment (*):Lucas cofactor, ECPP
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):c56 : Soule, Minovic, OpenPFGW, Primo
Decimal Digits:9591   (log10 is 9590.9499493164)
Rank (*):81183 (digit rank is 1)
Entrance Rank (*):58526
Currently on list? (*):short
Submitted:3/29/2012 10:37:04 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:105913
Status Flags:Verify
Score (*):32.3106 (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 313
Subcategory: "ECPP"
(archival tag id 214251, tag last modified 2023-03-11 16:02:30)
Lucas cofactor (archivable *)
Prime on list: yes, rank 15
Subcategory: "Lucas cofactor"
(archival tag id 214252, tag last modified 2023-03-11 15:53:59)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)
Donovan Johnson found that this cofactor was probably prime in 2004.

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 -tc -q"V(45953)/4561241750239" 2>&1 PFGW Version [GWNUM 26.5] Primality testing V(45953)/4561241750239 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.13% and helper 0.08% (0.48% proof) V(45953)/4561241750239 is Fermat and Lucas PRP! (32.4335s+0.0038s) [Elapsed time: 33.00 seconds]
modified2020-07-07 22:30:27
created2012-03-29 10:38:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"V(45953)/4561241750239" 2>&1 PFGW Version [GWNUM 26.5] V(45953)/4561241750239 1/1 mro=0 trial factoring to 2746508 V(45953)/4561241750239 has no small factor. [Elapsed time: 2.559 seconds]
modified2020-07-07 22:30:27
created2012-03-29 10:48:51

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