59 · 2727815 + 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:59 · 2727815 + 1
Verification status (*):Proven
Official Comment:Divides GF(727814,12)
Proof-code(s): (*):p227 : Harvey, Srsieve, PRP, OpenPFGW
Decimal Digits:219096   (log10 is 219095.91714619)
Rank (*):19703 (digit rank is 1)
Entrance Rank (*):525
Currently on list? (*):short
Submitted:10/15/2008 06:06:56 CDT
Last modified:10/15/2008 07:00:21 CDT
Database id:85635
Status Flags:none
Score (*):41.9688 (normalized score 0.1685)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 20, weight 46.0464279423424
Subcategory: "Divides GF(*,12)"
(archival tag id 187131, tag last modified 2016-03-15 13:57:15)

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_id85635
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 59 2 727815 1 2>&1
[Elapsed time: 10.008 seconds]
modified2011-12-27 16:48:46
created2008-10-15 06:22:01
id100742

fieldvalue
prime_id85635
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"59*2^727815+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 59*2^727815+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(98304,20) to FFT(98304,19)
Reduced from FFT(98304,19) to FFT(98304,18)
Reduced from FFT(98304,18) to FFT(98304,17)
Reduced from FFT(98304,17) to FFT(98304,16)
1455650 bit request FFT size=(98304,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
59*2^727815+1 is prime! (-1166.7973s+0.0000s)
[Elapsed time: 52.33 minutes]
modified2008-11-16 12:15:22
created2008-10-15 06:08:01
id100741

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.