(211279 + 1)/3

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:(211279 + 1)/3
Verification status (*):PRP
Official Comment (*):Cyclotomy, generalized Lucas number, Wagstaff
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):PM : Mihailescu
Decimal Digits:3395   (log10 is 3394.8401998393)
Rank (*):93129 (digit rank is 1)
Entrance Rank (*):6068
Currently on list? (*):short
Submitted:2/1/1998 05:59:59 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:28909
Status Flags:Verify
Score (*):29.0853 (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.
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 122
Subcategory: "Cyclotomy Proof"
(archival tag id 181336, tag last modified 2023-03-11 15:53:59)
Generalized Lucas Number (archivable *)
Prime on list: no, rank 106
Subcategory: "Generalized Lucas Number"
(archival tag id 181335, tag last modified 2023-03-11 16:02:31)
Wagstaff (archivable *)
Prime on list: yes, rank 8
Subcategory: "Wagstaff"
(archival tag id 181337, tag last modified 2023-03-11 16:02:31)

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.

Chris Caldwell writes (11 Sep 2014):  (report abuse)

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.
machineLinux PII 200
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing (2^11279+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Running N+1 test using discriminant 5, base 2+sqrt(5) Running N+1 test using discriminant 5, base 5+sqrt(5) Running N+1 test using discriminant 5, base 6+sqrt(5) Calling N+1 BLS with factored part 0.82% and helper 0.12% (2.62% proof) (2^11279+1)/3 is Fermat and Lucas PRP! (493.410000 seconds)
modified2003-03-25 17:22:57
created2003-01-05 00:01:29

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