3 · 2213321 + 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:3 · 2213321 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(213319); GF(213319,3), GF(213319,5), GF(213316,6), GF(213319,12) [g0]
Proof-code(s): (*):Y : Young
Decimal Digits:64217   (log10 is 64216.496826291)
Rank (*):51521 (digit rank is 1)
Entrance Rank (*):7
Currently on list? (*):no
Submitted:5/1997
Last modified:2/3/2014 21:20:04 CDT
Database id:401
Status Flags:none
Score (*):38.189 (normalized score 0.0018)

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.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 42, weight 39.287634372887
Subcategory: "Divides GF(*,6)"
(archival tag id 217609, tag last modified 2021-01-15 14:20:13)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 44, weight 39.287634372887
Subcategory: "Divides GF(*,5)"
(archival tag id 217608, tag last modified 2020-10-29 19:20:16)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 47, weight 39.287634372887
Subcategory: "Divides GF(*,3)"
(archival tag id 217607, tag last modified 2021-02-26 11:20:20)
Fermat Divisors (archivable *)
Prime on list: no, rank 34, weight 39.287634372887
Subcategory: "Divides Fermat"
(archival tag id 217606, tag last modified 2021-01-16 15:20:20)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 42, weight 39.287634372887
Subcategory: "Divides GF(*,12)"
(archival tag id 217610, tag last modified 2021-01-28 16:20:27)

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_id401
person_id9
machineWinXP P4 1.8GHz
whatprime
notesPFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 5 Primality testing 3*2^213321+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^213321+1 is prime! (362.352000 seconds)
modified2003-03-25 11:21:49
created2003-01-21 15:08:28
id67161

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.