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: 64670473 · 274146+1 Verification status (*): Proven Official Comment: Sophie Germain (p) Proof-code(s): (*): L446 : Saridis, NewPGen, Proth.exe, LLR Decimal Digits: 22328   (log10 is 22327.980764539) Rank (*): 34452 (digit rank is 1) Entrance Rank (*): 29931 Currently on list? (*): short Submitted: 1/6/2009 06:42:26 CDT Last modified: 1/6/2009 06:56:07 CDT Database id: 86168 Status Flags: none Score (*): 34.9268 (normalized score 0.0033)

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 16
Subcategory: "Sophie Germain (p)"
(archival tag id 192077, 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 86168 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 64670473 2 74146 1 2>&1 [Ellapsed time: 8.330 seconds] modified 2009-02-05 12:51:35 created 2009-01-06 06:52:10 id 101805

field value prime_id 86168 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"64670473*2^74146+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 64670473*2^74146+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) 148352 bit request FFT size=(8192,19) Calling Brillhart-Lehmer-Selfridge with factored part 99.97% 64670473*2^74146+1 is prime! (24.4202s+0.0003s) [Elapsed time: 24.00 seconds] modified 2009-02-05 12:51:35 created 2009-01-06 06:55:43 id 101807