6521953289619 · 255555 - 5
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
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, OpenPFGW, NewPGen, Primo
Decimal Digits:16737   (log10 is 16736.535786797)
Rank (*):60378 (digit rank is 3)
Entrance Rank (*):56919
Currently on list? (*):short
Submitted:4/30/2013 10:44:09 CDT
Last modified:10/21/2013 16:50:25 CDT
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 1
Subcategory: "Triplet (1)"
(archival tag id 217340, tag last modified 2013-10-21 16:50:28)
Elliptic Curve Primality Proof (archivable *)
Prime on list: yes, rank 17
Subcategory: "ECPP"
(archival tag id 217339, tag last modified 2014-03-03 10:52:10)

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 (1 May 2013): 
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.
fieldvalue
prime_id114016
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 6521953289619 2 55555 -5 2>&1
[Elapsed time: 8.499 seconds]
modified2013-06-04 07:30:39
created2013-04-30 10:48:01
id158391

fieldvalue
prime_id114016
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"6521953289619*2^55555-5" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [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]
modified2013-06-04 07:30:39
created2013-04-30 10:53:02
id158394

Query times: 0.0009 seconds to select prime, 0.0006 seconds to seek comments.