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): (*):c85 : Lasher, Broadhurst, Primo
Decimal Digits:12696   (log10 is 12695.658009707)
Rank (*):74382 (digit rank is 1)
Entrance Rank (*):68834
Currently on list? (*):short
Submitted:12/20/2016 19:55:55 CDT
Last modified:12/20/2016 20:50:32 CDT
Database id:122628
Blob database id:360
Status Flags:Verify, TrialDiv
Score (*):33.1796 (normalized score 0)

title='from prime_blob table' id='blob'>Description: (from blob table id=360)

The number of unrestricted integer partitions of 130060601 is p(130060601).

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 120
Subcategory: "ECPP"
(archival tag id 218548, tag last modified 2021-05-04 10:20:37)
Partitions (archivable *)
Prime on list: yes, rank 14
Subcategory: "Partitions"
(archival tag id 218549, 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 Broadhurst writes (22 Dec 2016):  (report abuse)

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 (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing 4549805440...0240447413 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 5+sqrt(5) Calling N+1 BLS with factored part 0.05% and helper 0.02% (0.15% proof) 4549805440...0240447413 is Fermat and Lucas PRP! (10.0469s+0.0644s) [Elapsed time: 11.00 seconds]
modified2020-07-07 17:30:16
created2016-12-20 20:43:01

Query times: 0.0006 seconds to select prime, 0.0013 seconds to seek comments.
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