6 · Bern(5534)/(89651360098907 · 22027790155387 · 114866371)
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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:6 · Bern(5534)/(89651360098907 · 22027790155387 · 114866371)
Verification status (*):PRP
Official Comment:Irregular, ECPP
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):c71 : Metcalfe, Ritschel, Andersen, TOPS, Primo
Decimal Digits:13862   (log10 is 13861.459704928)
Rank (*):70306 (digit rank is 1)
Entrance Rank (*):62174
Currently on list? (*):short
Submitted:2/12/2014 11:45:15 CDT
Last modified:2/12/2014 12:52:10 CDT
Database id:117141
Status Flags:Verify, TrialDiv
Score (*):33.4517 (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.
Irregular Primes (archivable *)
Prime on list: yes, rank 1
Subcategory: "Irregular Primes"
(archival tag id 217615, tag last modified 2014-02-12 12:52:14)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 79
Subcategory: "ECPP"
(archival tag id 217616, tag last modified 2019-06-02 14:20:07)

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 Metcalfe writes (11 Sep 2014): 
Certificate available from here.

David Broadhurst writes (11 Sep 2014): 
This number was reported as probably prime by Jens K. Andersen, in August 2005, at http://www.primenumbers.net/prptop/prptop.php from which list of PRPs it may now, happily, be removed.

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]
Primality testing 2882072674...2173601653 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
2882072674...2173601653 is Fermat and Lucas PRP! (94.5233s+0.0050s)
[Elapsed time: 1.58 minutes]
modified2014-02-12 12:29:38
created2014-02-12 12:28:03

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