(226903 - 1)/1113285395642134415541632833178044793

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.

Description:(226903 - 1)/1113285395642134415541632833178044793
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c55 : Gramolin, Primo
Decimal Digits:8063   (log10 is 8062.5633668362)
Rank (*):81051 (digit rank is 2)
Entrance Rank (*):58340
Currently on list? (*):no
Submitted:12/19/2011 05:02:03 CDT
Last modified:2/13/2012 10:20:01 CDT
Database id:103747
Status Flags:Verify
Score (*):31.7723 (normalized score 0)

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 314
Subcategory: "ECPP"
(archival tag id 213754, tag last modified 2022-06-26 16:37:20)
Mersenne cofactor (archivable *)
Prime on list: no, rank 21
Subcategory: "Mersenne cofactor"
(archival tag id 213755, tag last modified 2022-06-13 13:37:10)

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.

Alexander Gramolin writes (11 Sep 2014):  (report abuse)
The primality certificate can be found here.

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.
machineDitto P4 P4
notesPFGW Version [GWNUM 26.5] 3659037295654863....2288408027852599 1/1 mro=0 trial factoring to 2276301 3659037295...8027852599 has no small factor. [Elapsed time: 7.236 seconds]
modified2020-07-07 17:30:29
created2011-12-19 05:05:01

machineDitto P4 P4
notesPFGW Version [GWNUM 26.5] Primality testing 3659037295...8027852599 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 41, base 1+sqrt(41) Calling N+1 BLS with factored part 0.13% and helper 0.12% (0.51% proof) 3659037295...8027852599 is Fermat and Lucas PRP! (22.8656s+0.0241s) [Elapsed time: 23.00 seconds]
modified2020-07-07 17:30:29
created2011-12-19 05:08:02

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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