64670473 · 274146 + 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.

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 (*):67655 (digit rank is 1)
Entrance Rank (*):29931
Currently on list? (*):no
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)

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: no, rank 45
Subcategory: "Sophie Germain (p)"
(archival tag id 192077, tag last modified 2021-09-09 06:37:37)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 64670473 2 74146 1 2>&1 [Elapsed time: 8.330 seconds]
modified2020-07-07 17:30:38
created2009-01-06 06:52:10

machineRedHat P4 P4
notesCommand: /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]
modified2020-07-07 17:30:38
created2009-01-06 06:55:43

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.