394254311495 · 3733#/2 + 4

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:394254311495 · 3733#/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:1606   (log10 is 1605.8645036546)
Rank (*):105652 (digit rank is 1)
Entrance Rank (*):95075
Currently on list? (*):short
Submitted:11/30/2017 12:42:39 CDT
Last modified:11/30/2017 12:50:18 CDT
Database id:124040
Status Flags:Verify, TrialDiv
Score (*):26.7523 (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 4
Subcategory: "Quintuplet (5)"
(archival tag id 218948, tag last modified 2022-03-09 22:37:03)

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 (30 Nov 2017):  (report abuse)
Certificates are in FactorDB

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"394254311495*3733#/2+4" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 394254311495*3733#/2+4 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N+1 BLS with factored part 0.36% and helper 0.04% (1.12% proof) 394254311495*3733#/2+4 is Fermat and Lucas PRP! (0.4884s+0.0006s) [Elapsed time: 1.00 seconds]
modified2020-07-07 17:30:15
created2017-11-30 12:43:03

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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