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): (*):c77 : Batalov, Primo
Decimal Digits:16569   (log10 is 16568.376495635)
Rank (*):71077 (digit rank is 1)
Entrance Rank (*):65673
Currently on list? (*):short
Submitted:4/18/2017 09:42:43 CDT
Last modified:4/18/2017 10:20:19 CDT
Database id:123290
Blob database id:365
Status Flags:Verify, TrialDiv
Score (*):34.0039 (normalized score 0)

title='from prime_blob table' id='blob'>Description: (from blob table id=365)

The number of unrestricted integer partitions of 221444161 is p(221444161).

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 62
Subcategory: "ECPP"
(archival tag id 218706, tag last modified 2021-09-18 09:37:41)
Partitions (archivable *)
Prime on list: yes, rank 2
Subcategory: "Partitions"
(archival tag id 218707, 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.

Serge Batalov writes (18 Apr 2017):  (report abuse)
This is the largest known prime number of partitions of n2 (with n = 14881, n2 = 221444161). Extends OEIS A284594.

Certificate is available at factordb.com

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 2379554384...4199797591 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof) 2379554384...4199797591 is Fermat and Lucas PRP! (21.3673s+0.0056s) [Elapsed time: 21.00 seconds]
modified2020-07-07 17:30:16
created2017-04-18 10:13:02

Query times: 0.0005 seconds to select prime, 0.0011 seconds to seek comments.
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