16721795865536 + 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.

Description:16721795865536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5101 : Candido, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:538922   (log10 is 538921.06916304)
Rank (*):3785 (digit rank is 1)
Entrance Rank (*):3719
Currently on list? (*):yes
Submitted:5/23/2022 17:27:07 CDT
Last modified:5/23/2022 18:37:43 CDT
Database id:133964
Status Flags:TrialDiv
Score (*):44.7353 (normalized score 1.154)

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 Fermat (archivable *)
Prime on list: no, rank 704
Subcategory: "Generalized Fermat"
(archival tag id 227068, tag last modified 2022-06-23 12:37:21)

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_id133964
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"167217958^65536+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 167217958^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 41.51%


167217958^65536+1 is prime! (2846.5993s+0.0039s)
[Elapsed time: 47.45 minutes]
modified2022-05-23 18:18:28
created2022-05-23 17:31:01
id179691

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.