66982155216384 - 6698215528192 + 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:66982155216384 - 6698215528192 + 1
Verification status (*):Proven
Official Comment (*):Twin (p+2), generalized unique
Proof-code(s): (*):A18 : Trunov, Cyclo, PRST
Decimal Digits:144605   (log10 is 144604.51417575)
Rank (*):42395 (digit rank is 1)
Entrance Rank (*):42202
Currently on list? (*):short
Submitted:4/26/2024 09:36:37 UTC
Last modified:4/26/2024 19:37:18 UTC
Database id:138017
Status Flags:none
Score (*):40.6902 (normalized score 0.0132)

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.
Twin Primes (archivable *)
Prime on list: yes, rank 3
Subcategory: "Twin (p+2)"
(archival tag id 229510, tag last modified 2024-04-26 19:37:21)
Generalized Unique (archivable *)
Prime on list: no, rank 325
Subcategory: "Generalized Unique"
(archival tag id 229511, tag last modified 2024-04-26 19:37:21)

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_id138017
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"669821552^16384-669821552^8192+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 669821552^16384-669821552^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 48K, Pass1=128, Pass2=384, clm=1 on A 480366-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 43.18%


669821552^16384-669821552^8192+1 is prime! (272.7856s+0.0013s)
[Elapsed time: 4.58 minutes]
modified2024-04-26 18:15:31
created2024-04-26 18:10:56
id183859

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.