83 · 25318 - 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:83 · 25318 - 1
Verification status (*):Proven
Official Comment (*):Woodall
Proof-code(s): (*):K : Keller
Decimal Digits:1603   (log10 is 1602.7965950334)
Rank (*):103660 (digit rank is 1)
Entrance Rank (*):99
Currently on list? (*):short
Submitted:1984
Last modified:4/21/2021 11:19:46 CDT
Database id:38613
Status Flags:none
Score (*):26.7463 (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.
Woodall Primes (archivable *)
Prime on list: yes, rank 19
Subcategory: "Woodall Primes"
(archival tag id 176521, tag last modified 2018-03-28 13:50:05)

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_id38613
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"83*2^5318-1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 83*2^5318-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 99.89% 83*2^5318-1 is prime! (0.0201s+0.0001s) [Elapsed time: 0.00 seconds]
modified2021-04-22 09:31:56
created2021-04-21 11:19:46
id177931

Query times: 0.0005 seconds to select prime, 0.001 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.