1371371371371773785 · 2333333 - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Description:1371371371371773785 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L214 : Broadhurst, NewPGen, LLR
Decimal Digits:100362   (log10 is 100361.36869974)
Rank (*):43658 (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 0.0075)

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):  (report abuse)
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.
machineRedHat P4 P4
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]
modified2020-07-07 17:30:41
created2007-02-12 09:52:01

machineRedHat P4 P4
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]
modified2020-07-07 17:30:41
created2007-02-12 09:53:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.