225964951 - 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:225964951 - 1
Verification status (*):External
Official Comment (*):Mersenne 42
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):G8 : Nowak, GIMPS, Prime95
Decimal Digits:7816230   (log10 is 7816229.0869455)
Rank (*):13 (digit rank is 1)
Entrance Rank (*):1
Currently on list? (*):short
Submitted:2/18/2005 23:37:53 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:73550
Status Flags:none
Score (*):52.9329 (normalized score 2696.259)

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 10
Subcategory: "Mersenne"
(archival tag id 187007, 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)
Every Mersenne number less than this one has been checked once for primality (completed by GIMPS 8 April 2009), and then double checked (completed by GIMPS December 20, 2012). The residues for the tests were compared and they matched, providing a computational "proof" that this is the 42nd Mersenne prime by size.

Verification data:

Some of the very largest primes are externally verified by trusted groups or individuals and we do not reverify them at this site. This is one of those.
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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