3 · 220909 + 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.

Description:3 · 220909 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(20906,12) [D]; GF(20908,5) [g219]; GF(20908,5) [g151]; GF(20908,5) [g0]
Proof-code(s): (*):K : Keller
Decimal Digits:6295   (log10 is 6294.7133005929)
Rank (*):83690 (digit rank is 1)
Entrance Rank (*):8
Currently on list? (*):no
Submitted:1985
Last modified:1985
Database id:22329
Status Flags:none
Score (*):31.0043 (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.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 69, weight 32.102939759962
Subcategory: "Divides GF(*,5)"
(archival tag id 194843, tag last modified 2020-10-29 19:20:16)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 70, weight 32.102939759962
Subcategory: "Divides GF(*,12)"
(archival tag id 194842, tag last modified 2021-01-28 16:20:27)

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.
fieldvalue
prime_id22329
person_id9
machineLinux PII 200
whatprime
notesPFGW Version 1.1 for Pentium and compatibles Running N-1 test using base 5 Primality testing 3*2^20909+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^20909+1 is prime! (44.160000 seconds)
modified2003-03-25 11:26:01
created2002-12-08 19:26:41
id30493

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.