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 (*):Fibonacci number, cyclotomy
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p54 : Broadhurst, Water, OpenPFGW
Decimal Digits:7523   (log10 is 7522.9965763568)
Rank (*):80854 (digit rank is 1)
Entrance Rank (*):16901
Currently on list? (*):short
Submitted:7/23/2001 22:15:40 CDT
Last modified:7/23/2001 22:15:40 CDT
Database id:20235
Status Flags:Verify
Score (*):31.5575 (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.
Fibonacci Number (archivable *)
Prime on list: yes, rank 7
Subcategory: "Fibonacci Number"
(archival tag id 194580, tag last modified 2021-09-18 09:37:41)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 67
Subcategory: "Cyclotomy Proof"
(archival tag id 194579, tag last modified 2019-06-27 21:50:21)

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.
machineLinux PII 200
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 9921477614...0278699239 Running N-1 test using base 13 6792069340...5181224001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 71 Running N+1 test using discriminant 79, base 1+sqrt(79) Calling N-1 BLS with factored part 2.29% and helper 0.54% (7.42% proof) U(35999) is Fermat and Lucas PRP! (1007.860000 seconds)
modified2003-03-25 11:22:42
created2003-01-08 15:49:50

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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