6521953289619 · 255555 - 5

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:

Description:6521953289619 · 255555 - 5
Verification status (*):PRP
Official Comment (*):Triplet (1), ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c58 : Kaiser1, NewPGen, OpenPFGW, Primo
Decimal Digits:16737   (log10 is 16736.535786797)
Rank (*):76247 (digit rank is 3)
Entrance Rank (*):56919
Currently on list? (*):short
Submitted:4/30/2013 15:44:09 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:114016
Status Flags:Verify
Score (*):34.0351 (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.
Triplet (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Triplet (1)"
(archival tag id 217340, tag last modified 2024-07-11 00:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 140
Subcategory: "ECPP"
(archival tag id 217339, tag last modified 2024-07-11 00:37:12)

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.

Peter Kaiser writes (11 Sep 2014):  (report abuse)
Certificate can be found here: http://www.ellipsa.eu/public/primo/files/ecpp16737.7z

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/TrialDiv/TrialDiv -q 6521953289619 2 55555 -5 2>&1 [Elapsed time: 8.499 seconds]
modified2020-07-07 22:30:19
created2013-04-30 15:48:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"6521953289619*2^55555-5" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 6521953289619*2^55555-5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.20% proof) 6521953289619*2^55555-5 is Fermat and Lucas PRP! (46.6925s+0.0003s) [Elapsed time: 46.00 seconds]
modified2020-07-07 22:30:19
created2013-04-30 15:53:02

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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