224036583 - 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:224036583 - 1
Verification status (*):External
Official Comment (*):Mersenne 41
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):G7 : Findley_J, GIMPS, Prime95
Decimal Digits:7235733   (log10 is 7235732.4762669)
Rank (*):14 (digit rank is 1)
Entrance Rank (*):1
Currently on list? (*):short
Submitted:5/16/2004 13:29:07 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:70545
Status Flags:none
Score (*):52.6968 (normalized score 2158.2753)

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 11
Subcategory: "Mersenne"
(archival tag id 187008, 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 23 Feb 2009), and then double checked (completed by GIMPS December 1, 2011). The residues for the tests were compared and they matched, providing a computational "proof" that this is the 41st 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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