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 · 2303093+1 Verification status (*): Proven Official Comment: Divides Fermat F(303088); GF(303088,3), GF(303086,6), GF(303092,10), GF(303088,12), GF(303092,5) [g0] Proof-code(s): (*): Y : Young Decimal Digits: 91241   (log10 is 91240.5615970378) Rank (*): 14751 (digit rank is 1) Entrance Rank (*): 7 Currently on list? (*): short Submitted: 1/1998 Last modified: 1/1998 Database id: 223 Status Flags: none Score (*): 39.2718 (normalized score 0.2607)

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 23, weight 40.3704315773418
Subcategory: "Divides GF(*,5)"
(archival tag id 188453, tag last modified 2009-08-25 17:20:41)

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

Prime on list: no, rank 22, weight 40.3704315773418
Subcategory: "Divides GF(*,12)"
(archival tag id 188452, tag last modified 2009-06-27 09:50:03)

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

Prime on list: yes, rank 18, weight 40.3704315773418
Subcategory: "Divides GF(*,10)"
(archival tag id 188451, tag last modified 2009-10-20 10:20:04)

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

Prime on list: no, rank 21, weight 40.3704315773418
Subcategory: "Divides GF(*,6)"
(archival tag id 188450, tag last modified 2009-06-21 13:20:19)

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

Prime on list: no, rank 27, weight 40.3704315773418
Subcategory: "Divides GF(*,3)"
(archival tag id 188449, tag last modified 2009-04-16 13:50:04)

Prime Fermat Divisors (archivable *)

Prime on list: yes, rank 16, weight 40.3704315773418
Subcategory: "Divides Fermat"
(archival tag id 188448, tag last modified 2009-04-01 19:50:37)

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 223 person_id 9 machine WinXP P4 1.8GHz what prime notes PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 5 Primality testing 3*2^303093+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^303093+1 is prime! (798.688000 seconds) modified 2003-03-25 11:21:47 created 2003-01-22 16:03:19 id 67307