9 · 27967 + 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:9 · 27967 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(7964,6), GF(7966,10) [D]
Proof-code(s): (*):AR : Atkin, Rickert
Decimal Digits:2400   (log10 is 2399.2602179644)
Rank (*):95344 (digit rank is 2)
Entrance Rank (*):8
Currently on list? (*):no
Submitted:1979
Last modified:1979
Database id:32237
Status Flags:none
Score (*):28.0045 (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 68, weight 30.20180007356
Subcategory: "Divides GF(*,10)"
(archival tag id 175786, tag last modified 2021-02-18 04:50:24)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 75, weight 30.20180007356
Subcategory: "Divides GF(*,6)"
(archival tag id 175785, tag last modified 2022-05-12 21:37:21)

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_id32237
person_id9
machineLinux PII 200
whatprime
notesPFGW Version 1.1 for Pentium and compatibles Running N-1 test using base 5 Primality testing 9*2^7967+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.96% 9*2^7967+1 is prime! (5.880000 seconds)
modified2003-03-25 11:26:47
created2002-12-06 10:01:09
id22669

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.