(10859669 - 1)2 - 2

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:(10859669 - 1)2 - 2
Verification status (*):Proven
Official Comment (*):Near-repdigit
Proof-code(s): (*):p405 : Propper, Cksieve, OpenPFGW
Decimal Digits:1719338   (log10 is 1719338)
Rank (*):429 (digit rank is 1)
Entrance Rank (*):245
Currently on list? (*):short
Submitted:5/25/2022 10:49:34 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:133970
Status Flags:none
Score (*):48.2951 (normalized score 26.519)

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.
Near-repdigit (archivable *)
Prime on list: yes, rank 5
Subcategory: "Near-repdigit"
(archival tag id 227092, tag last modified 2024-02-07 04:37:20)

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.
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(10^859669-1)^2-2" 2>&1 PFGW Version [GWNUM 29.8] Primality testing (10^859669-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 17 Running N-1 test using base 19 Running N+1 test using discriminant 29, base 2+sqrt(29) Running N+1 test using discriminant 29, base 3+sqrt(29) Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof) (10^859669-1)^2-2 is prime! (466572.9025s+0.0126s) [Elapsed time: 5.40 days]
modified2022-07-11 18:21:44
created2022-05-25 10:51:02

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