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:7317   (log10 is 7316.2088358526)
Rank (*):80874 (digit rank is 2)
Entrance Rank (*):67923
Currently on list? (*):short
Submitted:9/8/2013 13:44:40 CDT
Last modified:9/8/2013 14:20:26 CDT
Database id:115423
Status Flags:Verify, TrialDiv
Score (*):31.471 (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 320
Subcategory: "ECPP"
(archival tag id 217238, tag last modified 2021-09-18 09:37:41)
Lucas cofactor (archivable *)
Prime on list: yes, rank 18
Subcategory: "Lucas cofactor"
(archival tag id 217239, 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 -tc -q"V(35107)/525110138418084707309" 2>&1 PFGW Version [GWNUM 26.5] Primality testing V(35107)/5251101384...8084707309 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.13% and helper 0.05% (0.45% proof) V(35107)/5251101384...8084707309 is Fermat and Lucas PRP! (25.1494s+0.0028s) [Elapsed time: 25.00 seconds]
modified2020-07-07 17:30:18
created2013-09-08 13:53:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.