285237 + 242619 + 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:285237 + 242619 + 1
Verification status (*):Proven
Official Comment (*):Gaussian Mersenne norm 31, generalized unique
Proof-code(s): (*):x16 : Doumen, Beelen, Unknown
Decimal Digits:25659   (log10 is 25658.893740411)
Rank (*):71746 (digit rank is 1)
Entrance Rank (*):942
Currently on list? (*):short
Submitted:8/8/2000 11:33:02 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:6642
Status Flags:none
Score (*):35.3567 (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.
Gaussian Mersenne norm (archivable *)
Prime on list: yes, rank 11
Subcategory: "Gaussian Mersenne norm"
(archival tag id 191714, tag last modified 2023-03-11 15:53:59)
Generalized Unique (archivable *)
Prime on list: no, rank 1532
Subcategory: "Generalized Unique"
(archival tag id 225583, tag last modified 2024-04-26 18:37:20)

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_id6642
person_id9
machineLinux PII 200
whatprime
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing 2^85237+2^42619+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^85237+2^42619+1 is prime! (-1659.897296 seconds)
modified2003-03-25 17:23:08
created2003-01-02 07:53:45
id59664

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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