At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help) value Description: primU(43359) Verification status (*): PRP Official Comment: Fibonacci primitive part, ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c8 : Water, Broadhurst, Primo Decimal Digits: 5939   (log10 is 5938.4758400585) Rank (*): 80329 (digit rank is 2) Entrance Rank (*): 68772 Currently on list? (*): short Submitted: 3/24/2013 06:38:33 CDT Last modified: 3/24/2013 07:20:36 CDT Database id: 111800 Status Flags: Verify Score (*): 30.8234 (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 351
Subcategory: "ECPP"
(archival tag id 215219, tag last modified 2018-09-22 16:20:28)

Fibonacci Primitive Part (archivable *)

Prime on list: yes, rank 18
Subcategory: "Fibonacci Primitive Part"
(archival tag id 215220, tag last modified 2018-07-22 00:50:24)

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): 

certificate

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.

field value prime_id 111800 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 2991162851944353....3160207078384001 1/1 mro=0 trial factoring to 1634386 2991162851...7078384001 has no small factor. [Elapsed time: 4.423 seconds] modified 2013-04-08 09:17:47 created 2013-03-24 06:48:17 id 153939

field value prime_id 111800 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 2991162851...7078384001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 43, base 3+sqrt(43) Calling N-1 BLS with factored part 1.15% and helper 0.04% (3.50% proof) 2991162851...7078384001 is Fermat and Lucas PRP! (17.0916s+0.0017s) [Elapsed time: 17.00 seconds] modified 2013-03-24 06:55:05 created 2013-03-24 06:54:48 id 153959