U(15631, 1, 5040) - U(15631, 1, 5039)
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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:U(15631, 1, 5040) - U(15631, 1, 5039)
Verification status (*):PRP
Official Comment:Lehmer number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:21134   (log10 is 21133.4992624487)
Rank (*):66154 (digit rank is 2)
Entrance Rank (*):10499
Currently on list? (*):short
Submitted:4/23/2003 07:08:03 CDT
Last modified:4/23/2003 07:08:03 CDT
Database id:64489
Status Flags:Verify
Score (*):34.7568 (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.
Lehmer number (archivable *)
Prime on list: yes, rank 13
Subcategory: "Lehmer number"
(archival tag id 192134, tag last modified 2019-08-03 12:50:11)

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): 
first non-trivial Konyagin-Pomerance proof above 20000 digits

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.
machineLinux P4 2.8GHz
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor')

Running N-1 test using base 59
6413180756...7639097601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 61
Running N+1 test using discriminant 83, base 12+sqrt(83)
Calling N-1 BLS with factored part 1.25% and helper 0.20% (3.96% proof)
3156911801...7639097601 is Fermat and Lucas PRP! (562.690000 seconds)
modified2003-07-12 13:12:12
created2003-04-24 07:13:29

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.