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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
Verification status (*):PRP
Official Comment:Lucas Aurifeuillian primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:5816   (log10 is 5815.8885923046)
Rank (*):79428 (digit rank is 1)
Entrance Rank (*):68575
Currently on list? (*):short
Submitted:2/26/2013 10:13:35 CDT
Last modified:2/26/2013 10:31:51 CDT
Database id:111355
Status Flags:Verify
Score (*):30.7586 (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.
Lucas Aurifeuillian primitive part (archivable *)
Prime on list: yes, rank 18
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 215105, tag last modified 2017-04-02 13:50:26)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 344
Subcategory: "ECPP"
(archival tag id 215106, tag last modified 2018-03-14 05:50:22)

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): 

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
notesPFGW Version [GWNUM 26.5]
7737351102917445....4545823891072801 1/1 mro=0

trial factoring to 1597757
7737351102...3891072801 has no small factor.
[Elapsed time: 4.033 seconds]
modified2013-02-26 10:34:48
created2013-02-26 10:18:12

machineRedHat Virtual STEM Server
notesPFGW Version [GWNUM 25.14]
Primality testing 7737351102...3891072801 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 17
Running N+1 test using discriminant 47, base 3+sqrt(47)
Calling N-1 BLS with factored part 1.85% and helper 0.16% (5.71% proof)
7737351102...3891072801 is Fermat and Lucas PRP! (8.2745s+0.0023s)
[Elapsed time: 9.00 seconds]
modified2013-02-26 10:30:51
created2013-02-26 10:30:42

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