2756839 - 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:2756839 - 1
Verification status (*):Proven
Official Comment (*):Mersenne 32
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):SG : Slowinski, Gage
Decimal Digits:227832   (log10 is 227831.24088833)
Rank (*):28208 (digit rank is 1)
Entrance Rank (*):1
Currently on list? (*):short
Submitted:2/20/1992 05:59:59 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:25
Status Flags:none
Score (*):42.0891 (normalized score 0.0567)

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 20
Subcategory: "Mersenne"
(archival tag id 187129, 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)
For more information see [Peterson92].

Chris Caldwell writes (11 Sep 2014):  (report abuse)
For an account by one of those running the machine whien it found this prime see http://t5k.org/notes/756839.html.

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_id25
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"2^756839-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^756839-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1513694 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2^756839-1 is prime! (9620.9778s+0.0007s) [Elapsed time: 2.67 hours]
modified2020-07-07 22:30:39
created2008-08-06 02:30:05
id100212

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