1371371371371773785 · 2333333 - 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:1371371371371773785 · 2333333 - 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L214 : Broadhurst, NewPGen, LLR
Decimal Digits:100362   (log10 is 100361.36869974)
Rank (*):41637 (digit rank is 2)
Entrance Rank (*):3052
Currently on list? (*):no
Submitted:2/12/2007 09:33:35 CDT
Last modified:2/12/2007 10:13:52 CDT
Removed (*):5/8/2008 20:41:36 CDT
Database id:79378
Status Flags:none
Score (*):39.5653 (normalized score 0.01)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): 
I agree with Jean Penne that LLR is totally reliable in detecting and proving primes of the form k*2^n-1 with k > 2^53, albeit without the speed-up of George Woltman's gwnums. This LLR proof resulted from a successful attempt to refute ill-informed hearsay in another place.

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_id79378
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"1371371371371773785*2^333333-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 34219777
1371371371371773785*2^333333-1 has no small factor.
[Elapsed time: 250.639 seconds]
modified2007-03-03 21:00:42
created2007-02-12 09:52:01
id87858

fieldvalue
prime_id79378
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/llr.pl 1371371371371773785*2^333333-1 2>&1
Starting Lucas Lehmer Riesel prime test of 1371371371371773785*2^333333-1
V1 = 4 ; Computing U0...
Done Computing U0.
Starting Lucas-Lehmer loop...
1371371371371773785*2^333333-1 is prime! Time: 1250.536 sec.
[Elapsed time: 1251 seconds]
modified2007-03-03 21:00:42
created2007-02-12 09:53:01
id87859

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.