120585 · 21205851 - 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:120585 · 21205851 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p260 : Harvey, Gcwsieve, MultiSieve, GenWoodall, OpenPFGW
Decimal Digits:363003   (log10 is 363002.4025947)
Rank (*):18941 (digit rank is 1)
Entrance Rank (*):1312
Currently on list? (*):no
Submitted:12/10/2012 20:32:55 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:110372
Status Flags:none
Score (*):43.5213 (normalized score 0.2354)

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.
Generalized Woodall (archivable *)
Prime on list: no, rank 48
Subcategory: "Generalized Woodall"
(archival tag id 214810, tag last modified 2024-02-26 15:37:18)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Steven Harvey writes (11 Sep 2014):  (report abuse)
241170*32^241170-1

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_id110372
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 120585 2 1205851 -1 2>&1 [Elapsed time: 10.406 seconds]
modified2020-07-07 22:30:23
created2012-12-10 20:35:01
id150729

fieldvalue
prime_id110372
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/llr.pl 120585*2^1205851-1 2>&1 Starting Lucas Lehmer Riesel prime test of 120585*2^1205851-1 Using Irrational Base DWT : Mersenne fftlen = 65536, Used fftlen = 114688 V1 = 9 ; Computing U0... V1 = 9 ; Computing U0...done. Starting Lucas-Lehmer loop... 120585*2^1205851-1 is prime! Time : 4286.960 sec. [Elapsed time: 71.45 minutes]
modified2020-07-07 22:30:23
created2012-12-10 20:53:02
id150730

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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