2618163402417 · 21290000 - 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:2618163402417 · 21290000 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (p)
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L927 : Brown1, TwinGen, PrimeGrid, LLR
Decimal Digits:388342   (log10 is 388341.11240328)
Rank (*):15850 (digit rank is 941)
Entrance Rank (*):3747
Currently on list? (*):short
Submitted:2/29/2016 14:11:16 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:121330
Status Flags:none
Score (*):43.7286 (normalized score 0.2722)

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 1
Subcategory: "Sophie Germain (p)"
(archival tag id 218236, tag last modified 2023-03-11 15:53:59)

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.

Dr. James Scott Brown writes (29 Feb 2016):  (report abuse)
Sophie Germain (p)

David Broadhurst writes (9 Mar 2016):  (report abuse)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/llr.pl 2618163402417*2^1290000-1 2>&1 Starting Lucas Lehmer Riesel prime test of 2618163402417*2^1290000-1 Using zero-padded AVX FFT length 128K, Pass1=128, Pass2=1K V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop... 2618163402417*2^1290000-1 is prime! (388342 decimal digits) Time : 783.407 sec. [Elapsed time: 13.07 minutes]
modified2020-07-07 22:30:16
created2016-02-29 14:40:05

Query times: 0.0003 seconds to select prime, 0.0007 seconds to seek comments.
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