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: 15 · 2403929+1 Verification status (*): Proven Official Comment: Divides GF(403927,10) Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p114 : Samidoost, FermFact, PRP, OpenPFGW Decimal Digits: 121596   (log10 is 121595.921209815) Rank (*): 7464 (digit rank is 1) Entrance Rank (*): 83 Currently on list? (*): short Submitted: 10/2002 Last modified: 10/23/2008 16:39:27 CDT Database id: 89 Status Flags: Duplicate Score (*): 40.1565 (normalized score 0.6312)

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 13, weight 42.86464582447
Subcategory: "Divides GF(*,10)"
(archival tag id 187541, tag last modified 2009-10-20 10:20:04)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Chris Caldwell writes (23 Oct 2008): 

Arkadiusz Wesolowski (math@wesolowski.ids.pl) notes that this prime divides GF(403927,10). (20 October 2008)

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 89 person_id 9 machine WinXP Athlon 1.3GHz what prime notes Running N-1 test using base 13 Primality testing 15*2^403929+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 15*2^403929+1 is prime! (3224.526000 seconds) modified 2003-03-25 11:26:14 created 2002-12-07 22:22:15 id 27782

field value prime_id 89 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 13 N-1: 15*2^403929+1Primality testing 15*2^403929+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 15*2^403929+1 is prime! (1326.705000 seconds) 312500/403934 modified 2003-03-25 11:21:47 created 2003-01-23 09:33:33 id 67357