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 cofactor, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:10708   (log10 is 10707.95528294)
Rank (*):80061 (digit rank is 1)
Entrance Rank (*):67247
Currently on list? (*):short
Submitted:9/25/2014 09:14:50 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:118553
Status Flags:Verify, TrialDiv
Score (*):32.6521 (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 257
Subcategory: "ECPP"
(archival tag id 217822, tag last modified 2023-03-11 16:02:30)
Lucas cofactor (archivable *)
Prime on list: yes, rank 12
Subcategory: "Lucas cofactor"
(archival tag id 217823, 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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"V(51349)/224417260052884218046541" 2>&1 PFGW Version [GWNUM 27.11] Primality testing V(51349)/2244172600...4218046541 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.21% and helper 0.11% (0.73% proof) V(51349)/2244172600...4218046541 is Fermat and Lucas PRP! (8.2136s+0.0017s) [Elapsed time: 8.00 seconds]
modified2020-07-07 22:30:17
created2014-09-25 09:21:00

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.