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: 33759183 · 2123458-1 Verification status (*): Proven Official Comment: Sophie Germain (p) Proof-code(s): (*): L527 : Tornberg, TwinGen, LLR Decimal Digits: 37173   (log10 is 37172.089596612) Rank (*): 27394 (digit rank is 3) Entrance Rank (*): 25529 Currently on list? (*): short Submitted: 6/26/2009 00:23:37 CDT Last modified: 6/27/2009 00:20:28 CDT Database id: 89021 Status Flags: none Score (*): 36.5019 (normalized score 0.0163)

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 6
Subcategory: "Sophie Germain (p)"
(archival tag id 210463, 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 89021 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 33759183 2 123458 -1 2>&1 [Ellapsed time: 8.558 seconds] modified 2009-07-10 15:55:50 created 2009-06-26 00:35:01 id 107407

field value prime_id 89021 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/llr.pl 33759183*2^123458-1 2>&1 Starting Lucas Lehmer Riesel prime test of 33759183*2^123458-1 Using Zero Padded IBDWT : Mersenne fftlen = 6144, Used fftlen = 12288 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done. Starting Lucas-Lehmer loop... 33759183*2^123458-1 is prime! Time : 39.357 sec. [Elapsed time: 40.00 seconds] modified 2009-07-10 15:55:50 created 2009-06-26 00:38:01 id 107409