(210169 - 1)/10402314702094700470118039921523041260063

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:(210169 - 1)/10402314702094700470118039921523041260063
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:3022   (log10 is 3021.1568959186)
Rank (*):95719 (digit rank is 2)
Entrance Rank (*):28029
Currently on list? (*):no
Submitted:7/8/2002 22:55:37 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:29464
Status Flags:Verify
Score (*):28.7224 (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.
Mersenne cofactor (archivable *)
Prime on list: no, rank 41
Subcategory: "Mersenne cofactor"
(archival tag id 175401, tag last modified 2023-10-16 19:37:15)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 734
Subcategory: "ECPP"
(archival tag id 175400, tag last modified 2024-03-24 06:37:14)

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_id29464
person_id9
machineLinux PII 200
whatprp
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 5 Primality testing (2^10169-1)/1040231470...3041260063 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N+1 test using discriminant 23, base 2+sqrt(23) Calling N-1 BLS with factored part 0.26% and helper 0.01% (0.80% proof) (2^10169-1)/1040231470...3041260063 is Fermat and Lucas PRP! (135.500000 seconds)
modified2003-03-25 17:22:57
created2003-01-04 21:57:53
id61886

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