6915957608192 - 6915957604096 - 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:6915957608192 - 6915957604096 - 1
Verification status (*):Proven
Official Comment (*):Twin (p)
Proof-code(s): (*):A13 : Marler, Cyclo, PRST
Decimal Digits:72417   (log10 is 72416.070222312)
Rank (*):54933 (digit rank is 2)
Entrance Rank (*):53596
Currently on list? (*):short
Submitted:1/13/2024 00:19:54 UTC
Last modified:1/13/2024 13:32:28 UTC
Database id:136882
Status Flags:none
Score (*):38.5595 (normalized score 0.0015)

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 13
Subcategory: "Twin (p)"
(archival tag id 229148, tag last modified 2024-05-06 08:37:28)

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_id136882
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"691595760^8192-691595760^4096-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 691595760^8192-691595760^4096-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2 on A 240561-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 36.54%


691595760^8192-691595760^4096-1 is prime! (270.6682s+0.0006s)
[Elapsed time: 4.60 minutes]
modified2024-01-13 03:57:11
created2024-01-13 03:52:35
id182720

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