237156667 - 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:237156667 - 1
Verification status (*):External
Official Comment (*):Mersenne 45
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):G11 : Elvenich, GIMPS, Prime95
Decimal Digits:11185272   (log10 is 11185271.305898)
Rank (*):9 (digit rank is 1)
Entrance Rank (*):2
Currently on list? (*):short
Submitted:9/6/2008 18:53:10 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:85528
Status Flags:none
Score (*):54.0294 (normalized score 8272.3336)

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 7
Subcategory: "Mersenne"
(archival tag id 187004, 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 (3 Sep 2016):  (report abuse)
The was the 46th mersenne prime found (though it is 45th in order of size). See the GIMPS press release.

Chris Caldwell writes (3 Sep 2016):  (report abuse)
Every Mersenne number less than this one has now been checked twice for primality by GIMPS (once by 25 December 2010, twice by 2 September 2016), and the residues compared. So this number is now 'proven' to be the 45th Mersenne prime 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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 37156667 -1 2>&1 [Elapsed time: 12.727 seconds]
modified2020-07-07 22:30:39
created2008-09-16 14:52:02

notesThis prime was first verified by Tom Duell (Burlington, MA, USA) and Rob Giltrap (Wellington, New Zealand), both of Sun Microsystems, using the Mlucas program by Ernst Mayer of Cupertino California USA. The verifications ran on 8 dual-core SPARC64 VI 2.15Ghz CPUs of a Sun SPARC Enterprise M5000 Server and 4 quad-core SPARC64 VII 2.52GHz CPUs of a Sun SPARC Enterprise M8000 Server in Menlo Park, CA, USA. The prime verification took 5 days. This prime was also independently verified by Tony Reix of Bull S.A. in Grenoble, France using 16 1.6 GHz Itanium2 CPUs of a Bull NovaScale 6160 HPC server and the Glucas program. Jeff Gilchrist of Carleton University in Ottawa, Canada has also verified primality using up to 16 1.6 GHz Itanium2 CPUs of a server at SHARCNET, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.
modified2020-07-07 22:30:39
created2008-09-16 15:14:32

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