8151728061 · 2125987 - 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:8151728061 · 2125987 - 1
Verification status (*):Proven
Official Comment:Twin (p)
Proof-code(s): (*):p35 : Augustin, NewPGen, OpenPFGW
Decimal Digits:37936   (log10 is 37935.777313401)
Rank (*):56568 (digit rank is 2)
Entrance Rank (*):28848
Currently on list? (*):short
Submitted:5/8/2010 13:59:24 CDT
Last modified:5/8/2010 14:20:25 CDT
Database id:92613
Status Flags:none
Score (*):36.5647 (normalized score 0.0006)

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 20
Subcategory: "Twin (p)"
(archival tag id 210663, tag last modified 2017-07-04 19:20:06)

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 8151728061 2 125987 -1 2>&1
[Elapsed time: 8.807 seconds]
modified2011-12-27 16:48:40
created2010-05-08 14:05:02

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 8151728061*2^125987-1 2>&1
Starting Lucas Lehmer Riesel prime test of 8151728061*2^125987-1
Using Zero Padded IBDWT : Mersenne fftlen = 6144, Used fftlen = 12288
V1 = 3 ; Computing U0...
V1 = 3 ; Computing U0...done.
Starting Lucas-Lehmer loop...

8151728061*2^125987-1 is prime! Time : 40.155 sec.
[Elapsed time: 40.00 seconds]
modified2010-10-13 12:41:38
created2010-05-08 14:08:01

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