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 (*):Fibonacci primitive part, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:6822   (log10 is 6821.4735104781)
Rank (*):88220 (digit rank is 1)
Entrance Rank (*):67798
Currently on list? (*):short
Submitted:4/30/2013 21:39:05 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:114023
Status Flags:Verify
Score (*):31.2537 (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 460
Subcategory: "ECPP"
(archival tag id 217115, tag last modified 2024-07-11 00:37:12)
Fibonacci Primitive Part (archivable *)
Prime on list: yes, rank 20
Subcategory: "Fibonacci Primitive Part"
(archival tag id 217116, tag last modified 2023-03-11 15:53:59)

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 2975161039...2382939201 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 43, base 9+sqrt(43) Calling N-1 BLS with factored part 0.94% and helper 0.05% (2.86% proof) 2975161039...2382939201 is Fermat and Lucas PRP! (23.2051s+0.0020s) [Elapsed time: 23.00 seconds]
modified2020-07-07 22:30:19
created2013-04-30 21:39:16

machineRedHat P4 P4
notesPFGW Version [GWNUM 26.5] 2975161039118578....6625072382939201 1/1 mro=0 trial factoring to 1899371 2975161039...2382939201 has no small factor. [Elapsed time: 5.099 seconds]
modified2020-07-07 22:30:19
created2013-04-30 21:48:08

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <> © Reginald McLean.