237156667 - 1
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
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 (*):4 (digit rank is 1)
Entrance Rank (*):2
Currently on list? (*):short
Submitted:9/6/2008 13:53:10 CDT
Last modified:3/15/2012 08:22:23 CDT
Database id:85528
Status Flags:none
Score (*):54.0294 (normalized score 38198.1278)

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 4
Subcategory: "Mersenne"
(archival tag id 187004, tag last modified 2013-02-05 07:54:28)

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): 
The was the 46th mersenne prime found (though it is not the 46th in order of size). See the GIMPS press release. I will add more information soon.

Chris Caldwell writes (11 Sep 2014): 
Every Mersenne number less than this one has been checked once for primality by GIMPS (by December 25, 2010), but not twice. Since single checks have a relatively high error rate, this may not be the 45th Mersenne prime by size. We will remove the question mark when GIMPS completes checking all lower exponents twice and comparing the residues.

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.
fieldvalue
prime_id85528
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 37156667 -1 2>&1
[Elapsed time: 12.727 seconds]
modified2011-12-27 16:48:46
created2008-09-16 09:52:02
id100523

fieldvalue
prime_id85528
person_id9
machine
whatprime
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.
modified2008-11-16 12:15:22
created2008-09-16 10:14:32
id100525

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.