22942396995 · 2265776 - 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:22942396995 · 2265776 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (p)
Proof-code(s): (*):L3494 : Batalov, NewPGen, LLR
Decimal Digits:80017   (log10 is 80016.908766381)
Rank (*):53950 (digit rank is 1)
Entrance Rank (*):52413
Currently on list? (*):short
Submitted:11/12/2023 19:38:19 UTC
Last modified:11/12/2023 20:37:14 UTC
Database id:136649
Status Flags:none
Score (*):38.8672 (normalized score 0.0021)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 4
Subcategory: "Sophie Germain (p)"
(archival tag id 228954, tag last modified 2024-05-06 21:37:14)

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.
machineUsing: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"22942396995*2^265776-1" >command_output 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 22942396995*2^265776-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 17, base 1+sqrt(17)
Special modular reduction using zero-padded AVX-512 FFT length 32K on 22942396995*2^265776-1
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%

22942396995*2^265776-1 is prime! (95.0310s+0.0002s)
[Elapsed time: 1.58 minutes]
modified2023-11-12 19:40:36
created2023-11-12 19:39:01

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.