40931485 · 253123 - 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:40931485 · 253123 - 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (p)
Proof-code(s): (*):p222 : Underbakke, TwinGen, LLR, OpenPFGW
Decimal Digits:16000   (log10 is 15999.228517159)
Rank (*):71289 (digit rank is 3)
Entrance Rank (*):27215
Currently on list? (*):no
Submitted:3/1/2007 10:22:33 CDT
Last modified:3/1/2007 10:52:18 CDT
Database id:79588
Status Flags:none
Score (*):33.8957 (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 (2nd kind) (archivable class *)
Prime on list: no, rank 23, weight 23.38139537532
Subcategory: "Cunningham chain 2nd kind (p)"
(archival tag id 212418, tag last modified 2020-05-31 14:50:18)

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 40931485*2^53123-1 2>&1 Starting Lucas Lehmer Riesel prime test of 40931485*2^53123-1 V1 = 4 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 40931485*2^53123-1 is prime! Time : 9.808 sec. [Elapsed time: 9 seconds]
modified2020-07-07 17:30:41
created2007-03-01 10:45:55

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 40931485 2 53123 -1 2>&1 [Elapsed time: 8.448 seconds]
modified2020-07-07 17:30:41
created2007-03-01 10:52:09

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.