p(130243561)

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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(130243561)
Verification status (*):	PRP
Official Comment (*):	Partitions, ECPP
Proof-code(s): (*):	c85 : Lasher, Broadhurst, Primo
Decimal Digits:	12705 (log₁₀ is 12704.590214594)
Rank (*):	79874 (digit rank is 3)
Entrance Rank (*):	69948
Currently on list? (*):	no
Submitted:	9/9/2017 15:33:34 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	123883
Blob database id:	377
Status Flags:	Verify
Score (*):	33.1818 (normalized score 0)

Description: (from blob table id=377)

The number of unrestricted integer partitions of 130243561 is p(130243561).

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 222
Subcategory: "ECPP"
(archival tag id 218873, tag last modified 2024-04-19 02:37:11)
Partitions (archivable *)
Prime on list: no, rank 33
Subcategory: "Partitions"
(archival tag id 218874, tag last modified 2023-03-11 15:53:59)

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.

field value

prime_id 123883

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prp

notes PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3892374278...0252864217 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.11% and helper 0.01% (0.35% proof) 3892374278...0252864217 is Fermat and Lucas PRP! (10.1791s+0.0740s) [Elapsed time: 10.00 seconds]

modified 2020-07-07 22:30:15

created 2017-09-09 16:13:02

id 169544

field	value
prime_id	123883
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prp
notes	PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3892374278...0252864217 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.11% and helper 0.01% (0.35% proof) 3892374278...0252864217 is Fermat and Lucas PRP! (10.1791s+0.0740s) [Elapsed time: 10.00 seconds]
modified	2020-07-07 22:30:15
created	2017-09-09 16:13:02
id	169544

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