289 · 218502 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:289 · 218502 + 1
Verification status (*):Proven
Official Comment (*):Cullen, generalized Fermat
Proof-code(s): (*):K : Keller
Decimal Digits:5573   (log10 is 5572.1178776177)
Rank (*):86220 (digit rank is 1)
Entrance Rank (*):7
Currently on list? (*):short
Last modified:1984
Database id:23436
Status Flags:none
Score (*):30.6257 (normalized score 0)

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.
Cullen primes (archivable *)
Prime on list: yes, rank 11
Subcategory: "Cullen primes"
(archival tag id 194999, tag last modified 2009-08-04 21:58:38)
Generalized Fermat (archivable *)
Prime on list: no, rank 6524
Subcategory: "Generalized Fermat"
(archival tag id 208628, tag last modified 2022-09-26 22:37:10)

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.
machineLinux PII 200
notesPFGW Version 1.1 for Pentium and compatibles Running N-1 test using base 3 Primality testing 289*2^18502+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.96% 289*2^18502+1 is prime! (35.000000 seconds)
modified2003-03-25 11:26:07
created2002-12-08 07:55:47

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.