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, PRP, NewPGen, Proth.exe Decimal Digits: 645817   (log10 is 645816.081408964) Rank (*): 189 (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 11.8592)

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 2013-03-05 15:20:04)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 2, weight 46.3896277016153
Subcategory: "Divides GF(*,10)"
(archival tag id 187037, tag last modified 2009-02-12 20:20:07)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 5, weight 46.3896277016153
Subcategory: "Divides GF(*,6)"
(archival tag id 187036, tag last modified 2013-05-20 20:50:27)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 4, weight 46.3896277016153
Subcategory: "Divides GF(*,5)"
(archival tag id 187035, tag last modified 2009-04-16 13:50:04)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 9, weight 46.3896277016153
Subcategory: "Divides GF(*,3)"
(archival tag id 187034, tag last modified 2013-04-28 21:50:30)

Fermat Divisors (archivable *)

Prime on list: yes, rank 5, weight 46.3896277016153
Subcategory: "Divides Fermat"
(archival tag id 187033, tag last modified 2013-05-14 17:50:05)

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.

field value prime_id 64011 person_id 9 machine Linux P4 2.8GHz what prime notes PFGW 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) modified 2003-03-25 11:21:40 created 2003-02-26 06:25:23 id 68493