566761969187 · 4733#/2 - 8

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.

Description:566761969187 · 4733#/2 - 8
Verification status (*):PRP
Official Comment (*):Quintuplet (1)
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 (*):100510 (digit rank is 6)
Entrance Rank (*):99014
Currently on list? (*):short
Submitted:12/6/2020 22:47:09 CDT
Last modified:12/6/2020 23:20:11 CDT
Database id:131444
Status Flags:Verify, TrialDiv
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 1
Subcategory: "Quintuplet (1)"
(archival tag id 225737, tag last modified 2020-12-06 23:20:13)

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 (6 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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"566761969187*4733#/2-8" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 566761969187*4733#/2-8 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N+1 BLS with factored part 0.58% and helper 0.03% (1.78% proof) 566761969187*4733#/2-8 is Fermat and Lucas PRP! (0.2054s+0.0002s) [Elapsed time: 0.00 seconds]
modified2021-04-20 17:39:26
created2020-12-06 22:51:01

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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