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 (*):Lucas cofactor, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:10305   (log10 is 10304.633719775)
Rank (*):77380 (digit rank is 1)
Entrance Rank (*):63613
Currently on list? (*):short
Submitted:6/16/2013 09:48:33 CDT
Last modified:6/16/2013 10:20:26 CDT
Database id:114432
Status Flags:Verify
Score (*):32.5331 (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 203
Subcategory: "ECPP"
(archival tag id 217185, tag last modified 2021-09-18 09:37:41)
Lucas cofactor (archivable *)
Prime on list: yes, rank 12
Subcategory: "Lucas cofactor"
(archival tag id 217186, tag last modified 2020-09-11 12:20:26)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"V(49391)/298414424560419239" 2>&1 PFGW Version [GWNUM 26.5] V(49391)/298414424560419239 1/1 mro=0 trial factoring to 2968100 V(49391)/298414424560419239 has no small factor. [Elapsed time: 2.761 seconds]
modified2020-07-07 17:30:19
created2013-06-16 09:52:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"V(49391)/298414424560419239" 2>&1 PFGW Version [GWNUM 26.5] Primality testing V(49391)/298414424560419239 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N-1 BLS with factored part 0.11% and helper 0.00% (0.35% proof) V(49391)/298414424560419239 is Fermat and Lucas PRP! (53.2562s+0.0042s) [Elapsed time: 53.00 seconds]
modified2020-07-07 17:30:19
created2013-06-16 09:53:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.