126831252923413 · 4657#/273 + 9

Previous Next Random

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:	126831252923413 · 4657#/273 + 9
Verification status (*):	PRP
Official Comment (*):	Quintuplet (4)
Proof-code(s): (*):	c88 : Kaiser1, PolySieve, Primo
Decimal Digits:	2002 (log₁₀ is 2001.0798847637)
Rank (*):	108236 (digit rank is 32)
Entrance Rank (*):	100998
Currently on list? (*):	yes
Submitted:	11/5/2020 11:48:06 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	131379
Status Flags:	Verify
Score (*):	27.4388 (normalized score 0)

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.

Quintuplet (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Quintuplet (4)"
(archival tag id 225709, 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 131379

person_id 9

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

what prp

notes PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1201945466...1933032479 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 96+sqrt(7) Calling N+1 BLS with factored part 0.11% and helper 0.06% (0.39% proof) 1201945466...1933032479 is Fermat and Lucas PRP! (0.6061s+0.0007s) [Elapsed time: 0.00 seconds]

modified 2021-04-20 22:39:26

created 2020-11-05 21:31:02

id 177075

field	value
prime_id	131379
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prp
notes	PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1201945466...1933032479 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 96+sqrt(7) Calling N+1 BLS with factored part 0.11% and helper 0.06% (0.39% proof) 1201945466...1933032479 is Fermat and Lucas PRP! (0.6061s+0.0007s) [Elapsed time: 0.00 seconds]
modified	2021-04-20 22:39:26
created	2020-11-05 21:31:02
id	177075

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.