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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:Lucas Aurifeuillian primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:8803   (log10 is 8802.5594073291)
Rank (*):76045 (digit rank is 2)
Entrance Rank (*):66927
Currently on list? (*):short
Submitted:11/23/2013 10:04:04 CDT
Last modified:11/23/2013 10:51:08 CDT
Database id:116406
Status Flags:Verify, TrialDiv
Score (*):32.0447 (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 14
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 217479, tag last modified 2019-04-07 01:20:28)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 224
Subcategory: "ECPP"
(archival tag id 217480, 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 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]
Primality testing 3625829090...8880249281 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 23
Running N+1 test using discriminant 37, base 3+sqrt(37)
Calling N-1 BLS with factored part 2.11% and helper 0.11% (6.44% proof)
3625829090...8880249281 is Fermat and Lucas PRP! (40.7123s+0.0066s)
[Elapsed time: 40.00 seconds]
modified2013-11-23 10:24:27
created2013-11-23 10:23:47

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.