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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 number
Proof-code(s): (*):p12 : Water, OpenPFGW
Decimal Digits:7409   (log10 is 7408.4028592215)
Rank (*):78014 (digit rank is 1)
Entrance Rank (*):14776
Currently on list? (*):short
Submitted:3/11/2001 09:28:29 CDT
Last modified:3/11/2001 09:28:29 CDT
Database id:20343
Status Flags:Verify
Score (*):31.5099 (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 Number (archivable *)
Prime on list: yes, rank 10
Subcategory: "Lucas Number"
(archival tag id 194604, tag last modified 2015-09-23 10:50:29)

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 PII 200
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 2528478246...1221068253 Running N-1 test using base 7 5276114048...6480314001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 17, base 6+sqrt(17) Calling N-1 BLS with factored part 0.63% and helper 0.33% (2.24% proof) V(35449) is Fermat and Lucas PRP! (957.260000 seconds)
modified2003-03-25 11:22:42
created2003-01-08 14:43:19

Query times: 0.0001 seconds to select prime, 0.0002 seconds to seek comments.