(3 · 21742059)^2 - 3 · 21742059 + 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:(3 · 21742059)^2 - 3 · 21742059 + 1
Verification status (*):Proven
Official Comment (*):Generalized unique
Proof-code(s): (*):A3 : Atnashev, PRST
Decimal Digits:1048825   (log10 is 1048824.9806753)
Rank (*):1577 (digit rank is 1)
Entrance Rank (*):1216
Currently on list? (*):short
Submitted:9/11/2023 07:41:18 UTC
Last modified:9/12/2023 04:37:16 UTC
Database id:136436
Status Flags:none
Score (*):46.7792 (normalized score 6.1225)

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 Unique (archivable *)
Prime on list: no, rank 28
Subcategory: "Generalized Unique"
(archival tag id 228809, tag last modified 2023-12-14 08:37:23)

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_id136436
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"Phi(3,-3*2^1742059)" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3,-3*2^1742059) [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 384K, Pass1=384, Pass2=1K, clm=4 on A 3484123-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%


Phi(3,-3*2^1742059) is prime! (35909.0796s+0.0630s)
[Elapsed time: 9.97 hours]
modified2023-09-12 03:51:06
created2023-09-11 17:52:37
id182268

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.