2329989 · 216309923 - 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:2329989 · 216309923 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):A20 : Propper, Batalov, Gcwsieve, PRST
Decimal Digits:4909783   (log10 is 4909782.4173237)
Rank (*):42 (digit rank is 1)
Entrance Rank (*):42
Currently on list? (*):short
Submitted:2/13/2024 17:12:24 UTC
Last modified:2/22/2024 23:37:25 UTC
Database id:137361
Status Flags:none
Score (*):51.5098 (normalized score 693.9738)

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 Woodall (archivable *)
Prime on list: yes, rank 1
Subcategory: "Generalized Woodall"
(archival tag id 229358, tag last modified 2024-02-22 23:37:28)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Ryan Propper writes (13 Feb 2024):  (report abuse)
= 2329989*(128^2329989)-1

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_id137361
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"2329989*2^16309923-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2329989*2^16309923-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 11, base 1+sqrt(11)
Special modular reduction using zero-padded FMA3 FFT length 1680K, Pass1=448, Pass2=3840, clm=2 on 2329989*2^16309923-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


2329989*2^16309923-1 is prime! (776457.0084s+0.0065s)
[Elapsed time: 8.99 days]
modified2024-02-22 23:29:43
created2024-02-13 23:48:46
id183203

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