(286371 - 1)/41681512921035887

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:(286371 - 1)/41681512921035887
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Proof-code(s): (*):E2 : Propper, CM
Decimal Digits:25984   (log10 is 25983.641812019)
Rank (*):67698 (digit rank is 1)
Entrance Rank (*):67182
Currently on list? (*):short
Submitted:6/13/2022 12:49:30 CDT
Last modified:6/13/2022 13:37:09 CDT
Database id:134046
Status Flags:Verify, TrialDiv
Score (*):35.3955 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 30
Subcategory: "ECPP"
(archival tag id 227127, tag last modified 2022-11-14 11:36:29)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 3
Subcategory: "Mersenne cofactor"
(archival tag id 227128, tag last modified 2022-11-14 11:36:30)

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.
fieldvalue
prime_id134046
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(2^86371-1)/41681512921035887" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (2^86371-1)/41681512921035887 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 17, base 6+sqrt(17) Calling N-1 BLS with factored part 0.05% and helper 0.02% (0.16% proof) (2^86371-1)/41681512921035887 is Fermat and Lucas PRP! (20.2377s+0.0001s) [Elapsed time: 20.00 seconds]
modified2022-07-11 13:21:44
created2022-06-13 12:51:01
id179780

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.