566761969187 · 4733#/2 + 4

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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:	566761969187 · 4733#/2 + 4
Verification status (*):	PRP
Official Comment (*):	Quintuplet (5)
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c67 : Batalov, NewPGen, OpenPFGW, Primo
Decimal Digits:	2034 (log₁₀ is 2033.9154042507)
Rank (*):	106207 (digit rank is 2)
Entrance Rank (*):	99014
Currently on list? (*):	yes
Submitted:	12/7/2020 04:47:09 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	131448
Status Flags:	Verify
Score (*):	27.4896 (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 2
Subcategory: "Quintuplet (5)"
(archival tag id 225733, 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.

Serge Batalov writes (7 Dec 2020): (report abuse)

Certificates: -8, -4, -2, +2, +4

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 131448

person_id 9

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

what prp

notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"566761969187*4733#/2+4" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 566761969187*4733#/2+4 [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 7 Running N-1 test using base 11 Running N-1 test using base 19 Running N-1 test using base 23 Running N-1 test using base 31 Running N-1 test using base 43 Running N+1 test using discriminant 59, base 74+sqrt(59) Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.22% proof) 566761969187*4733#/2+4 is Fermat and Lucas PRP! (0.5311s+0.0002s) [Elapsed time: 1.00 seconds]

modified 2021-04-20 22:39:26

created 2020-12-07 04:51:02

id 177141

field	value
prime_id	131448
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"5667619691874733#/2+4" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 5667619691874733#/2+4 [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 7 Running N-1 test using base 11 Running N-1 test using base 19 Running N-1 test using base 23 Running N-1 test using base 31 Running N-1 test using base 43 Running N+1 test using discriminant 59, base 74+sqrt(59) Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.22% proof) 566761969187*4733#/2+4 is Fermat and Lucas PRP! (0.5311s+0.0002s) [Elapsed time: 1.00 seconds]
modified	2021-04-20 22:39:26
created	2020-12-07 04:51:02
id	177141

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