p(141112026)

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:p(141112026)
Verification status (*):PRP
Official Comment (*):Partitions, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E6 : Lasher, Broadhurst, Underwood, CM
Decimal Digits:13225   (log10 is 13224.383249749)
Rank (*):79182 (digit rank is 1)
Entrance Rank (*):75504
Currently on list? (*):short
Submitted:7/12/2022 15:50:52 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:134155
Blob database id:430
Status Flags:Verify
Score (*):33.306 (normalized score 0)

Description: (from blob table id=430)

The number of unrestricted integer partitions of 141112026 is p(141112026).

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 192
Subcategory: "ECPP"
(archival tag id 227219, tag last modified 2024-03-24 06:37:14)
Partitions (archivable *)
Prime on list: yes, rank 16
Subcategory: "Partitions"
(archival tag id 227220, 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.

Charles H (Chuck) Lasher writes (13 Jul 2022):  (report abuse)
Certificate: http://factordb.com/index.php?id=1100000003738734390

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_id134155
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprp
notesPFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 2416760099...7411533629 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 2+sqrt(17)
Calling N+1 BLS with factored part 0.05% and helper 0.05% (0.21% proof)


2416760099...7411533629 is Fermat and Lucas PRP! (6.1450s+0.0008s)
[Elapsed time: 6.00 seconds]
modified2022-07-12 16:04:07
created2022-07-12 16:04:01
id179929

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