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: (156793499-1)/15678 Verification status (*): Proven Official Comment: Generalized repunit Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): x25 : Water, Broadhurst, Primo, OpenPFGW Decimal Digits: 14676   (log10 is 14675.2236513753) Rank (*): 39496 (digit rank is 1) Entrance Rank (*): 15357 Currently on list? (*): short Submitted: 5/22/2003 15:54:23 CDT Last modified: 5/22/2003 15:54:23 CDT Database id: 64777 Status Flags: none Score (*): 33.6283 (normalized score 0.0009)

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 Repunit (archivable *)

Prime on list: yes, rank 19
Subcategory: "Generalized Repunit"
(archival tag id 192557, tag last modified 2009-07-12 03:50:27)

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.

David Broadhurst writes (26 Nov 2005): 

helper

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 64777 person_id 9 machine Linux PII 200 what prime notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Running N-1 test using base 11 Primality testing (15679^3499-1)/15678 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 2+sqrt(17) Calling N-1 BLS with factored part 35.60% and helper 0.04% (106.85% proof) (15679^3499-1)/15678 is prime! (-202.347296 seconds) Helper File: 1332739 2495771 2534179 14869273 87164543 169093321 280581131119 372774240191 17519242514363 91406600732767 5960137883285191 346202087001776149 435072602647142021 1415697491214452543 14916118119135592943 402840969336893209981 20226331972667674284313 8760627760529248288064629 103003372673620241811483109 427076727834949318967389561 732214945285216501464215071 106744947338847372498642633384301856553513388747357 806111098417221911672523514114196605081493825576615584527263711415679802498015587201 65905313761712145019029525716874623...(147 digits)...51073506255502118326482181091630327 15376545960439194720127746549110733...(209 digits)...55509194229077290178626838353586621 phi(1749,15679)/(3499*1332739) modified 2005-12-30 08:30:48 created 2003-05-24 11:50:46 id 69654