3 · 22145353 + 1
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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:3 · 22145353 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(2145351), GF(2145351,3), GF(2145352,5), GF(2145348,6), GF(2145352,10), GF(2145351,12)
Proof-code(s): (*):g245 : Cosgrave, NewPGen, PRP, Proth.exe
Decimal Digits:645817   (log10 is 645816.081408964)
Rank (*):986 (digit rank is 1)
Entrance Rank (*):5
Currently on list? (*):short
Submitted:2/25/2003 10:47:15 CDT
Last modified:2/25/2003 10:47:15 CDT
Database id:64011
Status Flags:none
Score (*):45.291 (normalized score 4.6266)

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: yes, rank 5, weight 46.3896277016153
Subcategory: "Divides GF(*,12)"
(archival tag id 187038, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 5, weight 46.3896277016153
Subcategory: "Divides GF(*,10)"
(archival tag id 187037, tag last modified 2017-08-24 21:20:02)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 6, weight 46.3896277016153
Subcategory: "Divides GF(*,6)"
(archival tag id 187036, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 6, weight 46.3896277016153
Subcategory: "Divides GF(*,5)"
(archival tag id 187035, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 10, weight 46.3896277016153
Subcategory: "Divides GF(*,3)"
(archival tag id 187034, tag last modified 2016-03-15 13:57:15)
Fermat Divisors (archivable *)
Prime on list: yes, rank 7, weight 46.3896277016153
Subcategory: "Divides Fermat"
(archival tag id 187033, tag last modified 2016-03-15 13:57:14)

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_id64011
person_id9
machineLinux P4 2.8GHz
whatprime
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 5 Primality testing 3*2^2145353+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^2145353+1 is prime! (583.423264 seconds)
modified2003-03-25 11:21:40
created2003-02-26 06:25:23
id68493

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.