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 primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:16198   (log10 is 16197.562154611)
Rank (*):74067 (digit rank is 1)
Entrance Rank (*):68085
Currently on list? (*):short
Submitted:5/15/2019 02:45:07 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:126462
Status Flags:Verify, TrialDiv
Score (*):33.9338 (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 11
Subcategory: "Lucas primitive part"
(archival tag id 220257, tag last modified 2023-03-11 15:53:59)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 120
Subcategory: "ECPP"
(archival tag id 220258, tag last modified 2023-03-11 16:02:30)

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.

Serge Batalov writes (15 May 2019):  (report abuse)
Certificate is available at FactorDB

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
notesPFGW Version [GWNUM 27.11] Primality testing 3648838243...8552986081 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 37 Running N-1 test using base 43 Running N-1 test using base 53 Running N+1 test using discriminant 67, base 14+sqrt(67) Calling N-1 BLS with factored part 0.32% and helper 0.07% (1.04% proof) 3648838243...8552986081 is Fermat and Lucas PRP! (30.6440s+0.0019s) [Elapsed time: 30.00 seconds]
modified2020-07-07 22:30:13
created2019-05-15 02:51:02

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