18543637900515 · 2666667 - 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:18543637900515 · 2666667 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (p)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2429 : Bliedung, TwinGen, PrimeGrid, LLR
Decimal Digits:200701   (log10 is 200700.03231426)
Rank (*):30054 (digit rank is 101)
Entrance Rank (*):7743
Currently on list? (*):short
Submitted:4/11/2012 14:44:26 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:106226
Status Flags:none
Score (*):41.699 (normalized score 0.0446)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 2
Subcategory: "Sophie Germain (p)"
(archival tag id 214298, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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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 18543637900515 2 666667 -1 2>&1 [Elapsed time: 9.840 seconds]
modified2020-07-07 22:30:26
created2012-04-11 14:48:11

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/llr.pl 18543637900515*2^666667-1 2>&1 Starting Lucas Lehmer Riesel prime test of 18543637900515*2^666667-1 Using Zero Padded IBDWT : Mersenne fftlen = 32768, Used fftlen = 81920 V1 = 15 ; Computing U0... V1 = 15 ; Computing U0...done.Starting Lucas-Lehmer loop... 18543637900515*2^666667-1 is prime! Time : 940.863 sec. [Elapsed time: 16.05 minutes]
modified2020-07-07 22:30:26
created2012-04-11 15:05:01

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