612563306175 · 21290000 - 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:612563306175 · 21290000 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (1,d=175578398085*2^1290001) [p199]
Proof-code(s): (*):L2345 : Boerner, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.48155751)
Rank (*):13997 (digit rank is 1183)
Entrance Rank (*):1241
Currently on list? (*):no
Submitted:5/21/2013 19:08:29 CDT
Last modified:10/1/2015 20:25:34 CDT
Database id:114202
Status Flags:none
Score (*):43.7286 (normalized score 0.3963)

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 10
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 218095, tag last modified 2021-09-24 02:37:50)

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/TrialDiv/TrialDiv -q 612563306175 2 1290000 -1 2>&1 [Elapsed time: 10.320 seconds]
modified2020-07-07 17:30:19
created2013-05-21 19:18:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/llr.pl 612563306175*2^1290000-1 2>&1 Starting Lucas Lehmer Riesel prime test of 612563306175*2^1290000-1 Using Zero Padded IBDWT : Mersenne fftlen = 65536, Used fftlen = 131072 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done. Starting Lucas-Lehmer loop... 612563306175*2^1290000-1 is prime! Time : 5361.708 sec. [Elapsed time: 89.37 minutes]
modified2020-07-07 17:30:19
created2013-05-21 19:23:01

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