26767338410445 · 2666666 - 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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:26767338410445 · 2666666 - 1
Verification status (*):Proven
Official Comment:Arithmetic progression (3,d=12521740750545*2^666666)
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:200700   (log10 is 200699.89069451)
Rank (*):16881 (digit rank is 124)
Entrance Rank (*):2991
Currently on list? (*):short
Submitted:3/2/2011 02:53:54 CDT
Last modified:3/2/2011 03:50:57 CDT
Database id:98991
Status Flags:none
Score (*):41.699 (normalized score 0.1809)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 2, weight 48.7751007355278
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 213155, tag last modified 2012-02-13 15:51:05)

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_id98991
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 26767338410445 2 666666 -1 2>&1
[Elapsed time: 9.668 seconds]
modified2011-12-27 16:48:34
created2011-03-02 03:05:02
id127372

fieldvalue
prime_id98991
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 26767338410445*2^666666-1 2>&1
Starting Lucas Lehmer Riesel prime test of 26767338410445*2^666666-1
Using Zero Padded IBDWT : Mersenne fftlen = 32768, Used fftlen = 65536
V1 = 5 ; Computing U0...
V1 = 5 ; Computing U0...done.
Starting Lucas-Lehmer loop...

26767338410445*2^666666-1 is prime! Time : 1295.931 sec.
[Elapsed time: 21.60 minutes]
modified2011-03-25 10:27:29
created2011-03-02 03:08:01
id127373

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