12378188145 · 2140002 - 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:12378188145 · 2140002 - 1
Verification status (*):Proven
Official Comment (*):Twin (p)
Proof-code(s): (*):L95 : Urushi, LLR
Decimal Digits:42155   (log10 is 42154.894110028)
Rank (*):57933 (digit rank is 3)
Entrance Rank (*):31418
Currently on list? (*):no
Submitted:12/26/2010 06:17:47 CDT
Last modified:12/26/2010 06:50:23 CDT
Database id:97117
Status Flags:none
Score (*):36.8902 (normalized score 0.0005)

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: no, rank 21
Subcategory: "Twin (p)"
(archival tag id 213035, tag last modified 2021-02-21 08:50:13)

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/TrialDiv/TrialDiv -q 12378188145 2 140002 -1 2>&1 [Elapsed time: 9.014 seconds]
modified2020-07-07 17:30:32
created2010-12-26 06:18:29

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/llr.pl 12378188145*2^140002-1 2>&1 Starting Lucas Lehmer Riesel prime test of 12378188145*2^140002-1 Using Zero Padded IBDWT : Mersenne fftlen = 7168, Used fftlen = 14336 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop... 12378188145*2^140002-1 is prime! Time : 29.338 sec. [Elapsed time: 29.00 seconds]
modified2020-07-07 17:30:32
created2010-12-26 06:20:35

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.