64670473 · 274147 + 3

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.

This prime's information:

Description:64670473 · 274147 + 3
Verification status (*):Proven
Official Comment (*):Sophie Germain (2p+1)
Proof-code(s): (*):g422 : Saridis, NewPGen, Proth.exe
Decimal Digits:22329   (log10 is 22328.281794535)
Rank (*):72489 (digit rank is 1)
Entrance Rank (*):29931
Currently on list? (*):no
Submitted:1/6/2009 12:42:26 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:86169
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 (2p+1) (archivable *)
Prime on list: no, rank 51
Subcategory: "Sophie Germain (2p+1)"
(archival tag id 210489, tag last modified 2023-11-19 12:37:21)

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.
fieldvalue
prime_id86169
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 64670473 2 74147 3 2>&1 [Elapsed time: 8.410 seconds]
modified2020-07-07 22:30:38
created2009-01-06 12:52:01
id101804

fieldvalue
prime_id86169
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tc -hhelper_file_id_86169 -q"64670473*2^74147+3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 64670473*2^74147+3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_86169 Running N-1 test using base 2 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) 148354 bit request FFT size=(8192,19) Running N-1 test using base 5 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) 148354 bit request FFT size=(8192,19) Running N+1 test using discriminant 13, base 1+sqrt(13) 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) 148362 bit request FFT size=(8192,19) Calling N-1 BLS with factored part 100.00% and helper 0.02% (300.02% proof) 64670473*2^74147+3 is prime! (188.2700s+0.0000s) [Elapsed time: 3.13 minutes] Helper file contains: "64670473*2^74146+1"
modified2020-07-07 22:30:37
created2009-08-11 16:40:13
id108603

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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