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: 230402457-1 Verification status (*): External Official Comment: Mersenne 43?? Unofficial Comments: This prime has 3 user comments below. Proof-code(s): (*): G9 : Boone, Cooper, GIMPS, Prime95 Decimal Digits: 9152052   (log10 is 9152051.49888437) Rank (*): 5 (digit rank is 1) Entrance Rank (*): 1 Currently on list? (*): short Submitted: 12/15/2005 08:46:58 CDT Last modified: 12/25/2005 16:20:24 CDT Database id: 76545 Status Flags: none Score (*): 53.4157 (normalized score 330250.8857)

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.

Mersenne (archivable *)

Prime on list: yes, rank 5
Subcategory: "Mersenne"
(archival tag id 187006, tag last modified 2009-06-13 12:41:00)

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.

Chris Caldwell writes (25 Dec 2005): 

This prime was found 12/15/2005, but not announced until 12/25/2005 so that it could first be verified by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain. See notes.

Chris Caldwell writes (9 Aug 2007): 

The complete decimal expansion can be found at the GIMPS site and it may be found as an English name at Noll's site. The number of 0's, 1's, ... 9's in the decimal expansion are respectively: 913468, 914272, 916362, 913997, 914191, 916441, 915744, 915905, 916856, and 914816.

Chris Caldwell writes (9 Aug 2007): 

Not every Mersenne number less than this one has been checked for primality even once, so it is unknown if this is the 43rd Mersenne by size.

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.

field value prime_id 76545 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 30402457 -1 2>&1 [Elapsed time: 21.353 seconds] modified 2005-12-25 13:52:15 created 2005-12-25 03:22:00 id 81945