230402457 - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

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 9152051.4988844)
Rank (*):12 (digit rank is 1)
Entrance Rank (*):1
Currently on list? (*):short
Submitted:12/15/2005 14:46:58 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:76545
Status Flags:none
Score (*):53.4157 (normalized score 4502.6733)

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 9
Subcategory: "Mersenne"
(archival tag id 187006, tag last modified 2023-03-11 15:53:59)

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 (11 Sep 2014):  (report abuse)
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 (11 Sep 2014):  (report abuse)
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 (18 Jan 2015):  (report abuse)
Every Mersenne number less than this one has been checked once for primality by GIMPS (by December 25, 2010), and the a second time (January 25, 2013). Single checks have a relatively high error rate (a couple percent), but after a second check the residues from the two checks can be compared so the the error rate is extremely small.

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 P4 2.8GHz
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 30402457 -1 2>&1 [Elapsed time: 21.353 seconds]
modified2020-07-07 22:30:43
created2005-12-25 09:22:00

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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