56667641271 · 244441 + 5

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:56667641271 · 244441 + 5
Verification status (*):PRP
Official Comment (*):Triplet (3), ECPP
Proof-code(s): (*):c99 : Kruse, Schoeler, Primo
Decimal Digits:13389   (log10 is 13388.827372439)
Rank (*):75406 (digit rank is 1)
Entrance Rank (*):74941
Currently on list? (*):short
Submitted:4/2/2022 11:29:13 CDT
Last modified:4/2/2022 11:37:18 CDT
Database id:133793
Status Flags:Verify, TrialDiv
Score (*):33.3442 (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 152
Subcategory: "ECPP"
(archival tag id 226985, tag last modified 2022-08-07 13:37:22)
Triplet (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Triplet (3)"
(archival tag id 226986, tag last modified 2022-04-02 11:37:20)

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_id133793
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"56667641271*2^44441+5" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 56667641271*2^44441+5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 5+sqrt(5) Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof) 56667641271*2^44441+5 is Fermat and Lucas PRP! (4.4225s+0.3054s) [Elapsed time: 5.00 seconds]
modified2022-07-11 13:21:44
created2022-04-02 11:32:01
id179515

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