At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help) value Description: 2566851867 · 270001-1 Verification status (*): Proven Official Comment: Sophie Germain (p) Proof-code(s): (*): L109 : Nair, NewPGen, LLR Decimal Digits: 21082   (log10 is 21081.810127281) Rank (*): 34775 (digit rank is 1) Entrance Rank (*): 25683 Currently on list? (*): short Submitted: 6/26/2007 09:20:27 CDT Last modified: 6/26/2007 22:31:21 CDT Database id: 81358 Status Flags: none Score (*): 34.7492 (normalized score 0.0028)

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 19
Subcategory: "Sophie Germain (p)"
(archival tag id 192141, tag last modified 2009-11-18 16:20:05)

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.

field value prime_id 81358 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 2566851867 2 70001 -1 2>&1 [Elapsed time: 8.410 seconds] modified 2007-09-12 06:50:18 created 2007-06-26 09:22:10 id 91793

field value prime_id 81358 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 2566851867*2^70001-1 2>&1 Starting Lucas Lehmer Riesel prime test of 2566851867*2^70001-1 V1 = 3 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 2566851867*2^70001-1 is prime! Time : 18.448 sec. [Elapsed time: 19 seconds] modified 2007-09-12 06:50:18 created 2007-06-26 22:31:02 id 91836