(283339 + 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:(283339 + 1)/3
Verification status (*):PRP
Official Comment (*):ECPP, generalized Lucas number, Wagstaff
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:25088   (log10 is 25087.061687386)
Rank (*):71610 (digit rank is 2)
Entrance Rank (*):56573
Currently on list? (*):short
Submitted:9/17/2014 17:16:24 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:118512
Status Flags:Verify
Score (*):35.287 (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.
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 16
Subcategory: "Generalized Lucas Number"
(archival tag id 217818, tag last modified 2023-10-24 02:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 56
Subcategory: "ECPP"
(archival tag id 217819, tag last modified 2024-04-24 05:37:25)
Wagstaff (archivable *)
Prime on list: yes, rank 5
Subcategory: "Wagstaff"
(archival tag id 217820, tag last modified 2023-10-24 02:37:14)

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.

Tom Wu writes (12 May 2021):  (report abuse)
This number was originally reported as a probable prime by Richard McIntosh in July 2000. The certification process took approximately 18 months on a 6-core AMD Phenom II processor.

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 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^83339+1)/3" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (2^83339+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.10% proof) (2^83339+1)/3 is Fermat and Lucas PRP! (7.8406s+0.0003s) [Elapsed time: 8.00 seconds]
modified2020-07-07 22:30:17
created2014-09-17 17:21:01

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