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: 10495740081 · 283125-1 Verification status (*): Proven Official Comment: Sophie Germain (p) Proof-code(s): (*): L99 : Underbakke, TwinGen, LLR Decimal Digits: 25034   (log10 is 25033.1394026356) Rank (*): 33217 (digit rank is 2) Entrance Rank (*): 20065 Currently on list? (*): short Submitted: 2/9/2006 19:42:42 CDT Last modified: 2/10/2006 00:17:55 CDT Database id: 77012 Status Flags: none Score (*): 35.2803 (normalized score 0.0048)

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 13
Subcategory: "Sophie Germain (p)"
(archival tag id 191794, 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 77012 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 10495740081 2 83125 -1 2>&1 [Elapsed time: 13.815 seconds] modified 2006-03-10 10:52:00 created 2006-02-09 19:52:14 id 83016

field value prime_id 77012 person_id 9 machine WinXP Pentium M 1.7GHz what prime notes Command: pfgw.exe -n -tp -q"10495740081*2^83125-1" 2>&1 Primality testing 10495740081*2^83125-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.96% 10495740081*2^83125-1 is prime! (442.4620s+0.3242s) PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Running N+1 test using discriminant 7, base 1+sqrt(7) [Elapsed time: 444 seconds] modified 2006-03-10 10:52:00 created 2006-02-10 00:10:29 id 83019