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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
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c55 : Gramolin, Primo
Decimal Digits:5412   (log10 is 5411.3600318736)
Rank (*):81983 (digit rank is 1)
Entrance Rank (*):58539
Currently on list? (*):short
Submitted:3/26/2011 06:04:24 CDT
Last modified:3/26/2011 23:14:05 CDT
Database id:99271
Blob database id:251
Status Flags:Verify
Score (*):30.5347 (normalized score 0)

Description: (from blob table id=251)

For the primality proof certificate see: http://factordb.com/index.php?showid=1100000000293541437.

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 395
Subcategory: "ECPP"
(archival tag id 213180, tag last modified 2019-06-02 14:20:07)
Euler Irregular primes (archivable *)
Prime on list: yes, rank 6
Subcategory: "Euler Irregular primes"
(archival tag id 213179, 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.

Alexander Gramolin writes (11 Sep 2014): 
The primality certificate can be found here.

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 2291035789...0963774693 [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 0.20% and helper 0.18% (0.80% proof)
2291035789...0963774693 is Fermat and Lucas PRP! (10.0634s+0.0016s)
[Elapsed time: 10.00 seconds]
modified2011-03-27 14:30:13
created2011-03-27 14:30:13

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