100314512544015 · 2171960 - 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:100314512544015 · 2171960 - 1
Verification status (*):Proven
Official Comment:Twin (p)
Proof-code(s): (*):x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown
Decimal Digits:51780   (log10 is 51779.1194181454)
Rank (*):46249 (digit rank is 6)
Entrance Rank (*):10454
Currently on list? (*):short
Submitted:6/20/2006 03:35:53 CDT
Last modified:7/7/2006 10:39:14 CDT
Database id:77996
Status Flags:none
Score (*):37.5249 (normalized score 0.0025)

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.
Twin Primes (archivable *)
Prime on list: yes, rank 6
Subcategory: "Twin (p)"
(archival tag id 189942, tag last modified 2014-07-25 02:21:47)

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_id77996
person_id9
machineWinXP P4 2.2GHz By K
whatprime
notesCommand: pfgw.exe -n -f -tp -q"100314512544015*2^171960-1" 2>&1
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 100314512544015*2^171960-1 [N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 16858041
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling Brillhart-Lehmer-Selfridge with factored part 99.97%
100314512544015*2^171960-1 is prime! (1726.5873s+0.0416s)
[Elapsed time: 1727 seconds]
modified2006-07-14 06:27:04
created2006-06-20 07:56:31
id84543

fieldvalue
prime_id77996
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 100314512544015 2 171960 -1 2>&1
[Elapsed time: 9.501 seconds]
modified2006-07-14 06:27:03
created2006-07-07 10:39:04
id85235

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.