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 number,ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c76 : Kaiser1, Water, Underwood, Primo
Decimal Digits:29271   (log10 is 29270.181930491)
Rank (*):66681 (digit rank is 1)
Entrance Rank (*):55790
Currently on list? (*):short
Submitted:12/28/2014 03:17:48 CDT
Last modified:12/28/2014 03:50:20 CDT
Database id:119012
Status Flags:Verify, TrialDiv
Score (*):35.7636 (normalized score 0.0001)

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 22
Subcategory: "ECPP"
(archival tag id 217872, tag last modified 2022-10-15 20:37:20)
Lucas Number (archivable *)
Prime on list: yes, rank 2
Subcategory: "Lucas Number"
(archival tag id 217873, tag last modified 2015-09-23 10:50:29)

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.

Paul Underwood writes (28 Dec 2014):  (report abuse)
The certificate is here: http://www.ellipsa.eu/public/primo/top20.html

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"V(140057)" 2>&1 PFGW Version [GWNUM 27.11] Primality testing V(140057) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 37, base 1+sqrt(37) Calling N-1 BLS with factored part 0.38% and helper 0.20% (1.34% proof) V(140057) is Fermat and Lucas PRP! (63.6931s+0.0077s) [Elapsed time: 63.00 seconds]
modified2020-07-07 17:30:17
created2014-12-28 03:21:02

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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