89725 · 21256151 - 1
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:89725 · 21256151 - 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:378145   (log10 is 378144.08299677)
Rank (*):9766 (digit rank is 2)
Entrance Rank (*):1140
Currently on list? (*):no
Submitted:12/10/2012 15:30:19 CDT
Last modified:12/10/2012 17:20:48 CDT
Database id:110373
Status Flags:none
Score (*):43.6469 (normalized score 0.7799)

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 24
Subcategory: "Generalized Woodall"
(archival tag id 214811, tag last modified 2018-09-26 16:50:25)

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): 

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 89725 2 1256151 -1 2>&1
[Elapsed time: 10.761 seconds]
modified2012-12-19 19:14:49
created2012-12-10 15:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 89725*2^1256151-1 2>&1
Starting Lucas Lehmer Riesel prime test of 89725*2^1256151-1
Using Irrational Base DWT : Mersenne fftlen = 65536, Used fftlen = 114688
V1 = 4 ; Computing U0...
V1 = 4 ; Computing U0...done.
Starting Lucas-Lehmer loop...

89725*2^1256151-1 is prime! Time : 4431.614 sec.
[Elapsed time: 73.85 minutes]
modified2012-12-19 19:14:49
created2012-12-10 15:38:02

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.