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
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:5479   (log10 is 5478.6293192481)
Rank (*):83313 (digit rank is 1)
Entrance Rank (*):69839
Currently on list? (*):no
Submitted:5/11/2013 15:51:55 CDT
Last modified:5/11/2013 16:20:30 CDT
Database id:114125
Status Flags:Verify
Score (*):30.5731 (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 406
Subcategory: "ECPP"
(archival tag id 217147, tag last modified 2020-09-18 15:20:29)
Lucas cofactor (archivable *)
Prime on list: no, rank 23
Subcategory: "Lucas cofactor"
(archival tag id 217148, tag last modified 2020-09-11 12:20:26)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014):  (report abuse)

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(26309)/42316339086094085101" 2>&1 PFGW Version [GWNUM 26.5] V(26309)/42316339086094085101 1/1 mro=0 trial factoring to 1497521 V(26309)/42316339086094085101 has no small factor. [Elapsed time: 0.798 seconds]
modified2020-07-07 17:30:19
created2013-05-11 15:52:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"V(26309)/42316339086094085101" 2>&1 PFGW Version [GWNUM 26.5] Primality testing V(26309)/42316339086094085101 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 0.20% and helper 0.04% (0.64% proof) V(26309)/42316339086094085101 is Fermat and Lucas PRP! (10.1923s+0.0020s) [Elapsed time: 10.00 seconds]
modified2020-07-07 17:30:19
created2013-05-11 15:53:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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