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.

Verification status (*):PRP
Official Comment (*):Partitions, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c59 : Metcalfe, OpenPFGW, Primo
Decimal Digits:11138   (log10 is 11137.675401908)
Rank (*):77994 (digit rank is 1)
Entrance Rank (*):69799
Currently on list? (*):short
Submitted:3/21/2016 08:45:48 CDT
Last modified:3/21/2016 09:50:35 CDT
Database id:121457
Blob database id:352
Status Flags:Verify, TrialDiv
Score (*):32.774 (normalized score 0)

title='from prime_blob table' id='blob'>Description: (from blob table id=352)

The number of unrestricted integer partitions of 100115477 is p(100115477).

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 169
Subcategory: "ECPP"
(archival tag id 218290, tag last modified 2022-05-26 15:37:30)
Partitions (archivable *)
Prime on list: yes, rank 20
Subcategory: "Partitions"
(archival tag id 218291, tag last modified 2020-02-10 21:20:08)

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.

David Metcalfe writes (21 Mar 2016):  (report abuse)
Certificate available from here. Note that the certificate uses the new format introduced with Primo 4.2.0.

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing 4735893292...3093070911 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.11% and helper 0.11% (0.46% proof) 4735893292...3093070911 is Fermat and Lucas PRP! (9.3801s+0.0034s) [Elapsed time: 10.00 seconds]
modified2020-07-07 17:30:16
created2016-03-21 09:21:01

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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