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:6941   (log10 is 6940.9177590965)
Rank (*):82622 (digit rank is 1)
Entrance Rank (*):67845
Currently on list? (*):short
Submitted:5/23/2013 15:25:02 CDT
Last modified:5/23/2013 15:50:36 CDT
Database id:114223
Status Flags:Verify
Score (*):31.3076 (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 345
Subcategory: "ECPP"
(archival tag id 217160, tag last modified 2021-09-18 09:37:41)
Lucas cofactor (archivable *)
Prime on list: yes, rank 20
Subcategory: "Lucas cofactor"
(archival tag id 217161, 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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"V(33353)/279902102741094707003083072429" 2>&1 PFGW Version [GWNUM 26.5] V(33353)/2799021....4707003083072429 1/1 mro=0 trial factoring to 1935450 V(33353)/2799021027...3083072429 has no small factor. [Elapsed time: 1.261 seconds]
modified2020-07-07 17:30:19
created2013-05-23 15:35:04

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"V(33353)/279902102741094707003083072429" 2>&1 PFGW Version [GWNUM 26.5] Primality testing V(33353)/2799021027...3083072429 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 17 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N-1 BLS with factored part 0.11% and helper 0.10% (0.44% proof) V(33353)/2799021027...3083072429 is Fermat and Lucas PRP! (23.9859s+0.0028s) [Elapsed time: 24.00 seconds]
modified2020-07-07 17:30:19
created2013-05-23 15:38:28

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