272879344275 · 236622 - 1

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:272879344275 · 236622 - 1
Verification status (*):Proven
Official Comment (*):Cunningham chain (4p+3)
Proof-code(s): (*):p395 : Angel, Augustin, NewPGen, OpenPFGW
Decimal Digits:11036   (log10 is 11035.756471869)
Rank (*):78957 (digit rank is 1)
Entrance Rank (*):70476
Currently on list? (*):short
Submitted:8/30/2016 14:05:54 CDT
Last modified:8/30/2016 14:20:46 CDT
Database id:122110
Status Flags:TrialDiv
Score (*):32.7455 (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.
Cunningham Chains (1st kind) (archivable class *)
Prime on list: yes, rank 4, weight 41.838280939725
Subcategory: "Cunningham chain (4p+3)"
(archival tag id 218389, tag last modified 2020-02-18 11:20:24)

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 -tp -q"272879344275*2^36622-1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 272879344275*2^36622-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 99.90% 272879344275*2^36622-1 is prime! (1.9265s+0.0001s) [Elapsed time: 2.00 seconds]
modified2020-07-07 17:30:16
created2016-08-30 14:13:06

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