2^30402457 - 1

This prime's information:

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 187006, tag last modified 2024-10-21 21:37:25)

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.