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.

Verification status (*):PRP
Official Comment (*):ECPP, Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c69 : Jacobsen, Primo
Decimal Digits:18689   (log10 is 18688.694824825)
Rank (*):69594 (digit rank is 1)
Entrance Rank (*):58147
Currently on list? (*):short
Submitted:12/24/2013 16:32:04 CDT
Last modified:12/24/2013 16:50:59 CDT
Database id:116718
Status Flags:Verify, TrialDiv
Score (*):34.3765 (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.
Lucas primitive part (archivable *)
Prime on list: yes, rank 2
Subcategory: "Lucas primitive part"
(archival tag id 217547, tag last modified 2013-12-24 16:51:02)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 43
Subcategory: "ECPP"
(archival tag id 217548, tag last modified 2021-09-18 09:37:41)

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.
machineDitto P4 P4
notesPFGW Version [GWNUM 26.5] Primality testing 4952503885...1032588881 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N+1 test using discriminant 37, base 12+sqrt(37) Calling N-1 BLS with factored part 0.48% and helper 0.04% (1.48% proof) 4952503885...1032588881 is Fermat and Lucas PRP! (137.4025s+0.0076s) [Elapsed time: 2.28 minutes]
modified2020-07-07 17:30:18
created2013-12-24 16:38:03

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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