65516468355 · 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.

This prime's information:

Description:65516468355 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):Twin (p)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L923 : Kaiser1, Klahn, NewPGen, PrimeGrid, TPS, SunGard, LLR
Decimal Digits:100355   (log10 is 100354.04789514)
Rank (*):48760 (digit rank is 11)
Entrance Rank (*):9406
Currently on list? (*):short
Submitted:8/13/2009 20:59:57 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:89650
Status Flags:none
Score (*):39.5651 (normalized score 0.0042)

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 5
Subcategory: "Twin (p)"
(archival tag id 210492, tag last modified 2024-04-26 18:37:21)

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.

John Michael Blazek writes (11 Sep 2014):  (report abuse)
Credit will be as follows once all users have responded:
  1. (SG Grid) (United States), discoverer
  2. Peter Kaiser (Germany), top siever
  3. Keith Klahn (United States), top producer by M tested and by single primes found
  4. TPS, et al.
  5. PrimeGrid, et al.
  6. LLR, primality program developed by Jean Penne
  7. NewPGen, sieving program developed by Paul Jobling
  8. tpsieve, sieving program developed by Geoff Reynolds

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 65516468355 2 333333 -1 2>&1 [Elapsed time: 10.082 seconds]
modified2020-07-07 22:30:37
created2009-08-13 21:05:11

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 65516468355*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 65516468355*2^333333-1 Using Zero Padded IBDWT : Mersenne fftlen = 16384, Used fftlen = 32768 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done. Starting Lucas-Lehmer loop... 65516468355*2^333333-1 is prime! Time : 550.975 sec. [Elapsed time: 9.18 minutes]
modified2020-07-07 22:30:37
created2009-08-13 21:08:02

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