334310 · 211334310 - 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:334310 · 211334310 - 1
Verification status (*):Proven
Official Comment:Generalized Woodall
Proof-code(s): (*):p350 : Koen, Gcwsieve, GenWoodall, OpenPFGW
Decimal Digits:777037   (log10 is 777036.39177994)
Rank (*):517 (digit rank is 1)
Entrance Rank (*):78
Currently on list? (*):short
Submitted:4/11/2012 23:40:42 CDT
Last modified:4/14/2012 02:20:22 CDT
Database id:106236
Status Flags:none
Score (*):45.8588 (normalized score 8.3657)

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: yes, rank 2
Subcategory: "Generalized Woodall"
(archival tag id 214301, tag last modified 2015-05-01 14:20:30)

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_id106236
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 334310 211 334310 -1 2>&1
[Elapsed time: 9.873 seconds]
modified2012-07-16 11:33:01
created2012-04-11 23:48:01
id142062

fieldvalue
prime_id106236
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"334310*211^334310-1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 334310*211^334310-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
334310*211^334310-1 is prime! (180542.2381s+0.0672s)
[Elapsed time: 2.09 days]
modified2012-07-16 11:33:01
created2012-04-11 23:53:01
id142063

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.