26273597661 · 2333333 - 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.

Description:26273597661 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (3,d=38478921*2^333341) [g282]
Proof-code(s): (*):L329 : Schoenrogge, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.65106421)
Rank (*):44626 (digit rank is 916)
Entrance Rank (*):4145
Currently on list? (*):no
Submitted:11/17/2007 20:55:17 CDT
Last modified:1/4/2008 08:40:48 CDT
Database id:83042
Status Flags:none
Score (*):39.5651 (normalized score 0.0075)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 34, weight 46.294612968121
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 188194, tag last modified 2021-09-24 19:37:50)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/llr.pl 26273597661*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 26273597661*2^333333-1 V1 = 5 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 26273597661*2^333333-1 is prime! Time: 1280.299 sec. [Elapsed time: 21.33 minutes]
modified2020-07-07 17:30:40
created2007-11-17 21:05:43

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 26273597661 2 333333 -1 2>&1 [Elapsed time: 9.583 seconds]
modified2020-07-07 17:30:40
created2007-11-17 21:22:02

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.