(2637113681 - 1)/26370
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:(2637113681 - 1)/26370
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p170 : Wu_T, Primo, OpenPFGW
Decimal Digits:60482   (log10 is 60481.011887298)
Rank (*):48557 (digit rank is 1)
Entrance Rank (*):31809
Currently on list? (*):short
Submitted:2/16/2012 01:33:47 CDT
Last modified:2/16/2012 02:20:25 CDT
Database id:104672
Status Flags:Verify
Score (*):38.0041 (normalized score 0.0026)

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.
Generalized Repunit (archivable *)
Prime on list: yes, rank 6
Subcategory: "Generalized Repunit"
(archival tag id 214045, tag last modified 2018-09-09 08:20:06)

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.

Tom Wu writes (11 Sep 2014): 
For details of the N-1 primality proof, see:
N-1 was factored to 32.43%, and the KP proof used 30.09%. This proof also relies on an ECPP certificate of a 15267-digit helper prime that divides N-1.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"(26371^13681-1)/26370" 2>&1
PFGW Version [GWNUM 26.5]
(26371^13681-1)/26370 1/1 mro=0

trial factoring to 19909641
(26371^13681-1)/26370 has no small factor.
[Elapsed time: 95.478 seconds]
modified2012-02-19 19:07:47
created2012-02-16 01:35:07

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"(26371^13681-1)/26370" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing (26371^13681-1)/26370 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 29
Running N+1 test using discriminant 67, base 3+sqrt(67)
Calling N-1 BLS with factored part 0.48% and helper 0.00% (1.45% proof)
(26371^13681-1)/26370 is Fermat and Lucas PRP! (1541.1355s+0.0037s)
[Elapsed time: 25.68 minutes]
modified2012-02-19 19:07:47
created2012-02-16 01:39:33

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