3 · 2157169 + 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 · 2157169 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(157167); GF(157167,3), GF(157168,5), GF(157163,6), GF(157168,10), GF(157167,12) [g0]
Proof-code(s): (*):Y : Young
Decimal Digits:47314   (log10 is 47313.060509767)
Rank (*):57545 (digit rank is 1)
Entrance Rank (*):5
Currently on list? (*):no
Submitted:8/1995
Last modified:9/2/2007 17:02:55 CDT
Database id:1180
Status Flags:none
Score (*):37.2466 (normalized score 0.0007)

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 48, weight 38.345216763994
Subcategory: "Divides GF(*,12)"
(archival tag id 190387, tag last modified 2021-01-28 16:20:27)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 37, weight 38.345216763994
Subcategory: "Divides GF(*,10)"
(archival tag id 190386, tag last modified 2021-02-18 04:50:24)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 43, weight 38.345216763994
Subcategory: "Divides GF(*,6)"
(archival tag id 190385, tag last modified 2021-01-15 14:20:13)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 46, weight 38.345216763994
Subcategory: "Divides GF(*,5)"
(archival tag id 190384, tag last modified 2020-10-29 19:20:16)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 50, weight 38.345216763994
Subcategory: "Divides GF(*,3)"
(archival tag id 190383, tag last modified 2021-02-26 11:20:20)
Fermat Divisors (archivable *)
Prime on list: no, rank 35, weight 38.345216763994
Subcategory: "Divides Fermat"
(archival tag id 190382, tag last modified 2021-01-16 15:20:20)

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_id1180
person_id9
machineWinXP Athlon 1.3GHz
whatprime
notesPFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 5 Primality testing 3*2^157169+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^157169+1 is prime! (302.515000 seconds)
modified2003-03-25 11:21:55
created2003-01-19 16:29:48
id66213

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.