15859176262144 + 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:15859176262144 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5544 : Byerly, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1887511   (log10 is 1887510.3625342)
Rank (*):222 (digit rank is 1)
Entrance Rank (*):208
Currently on list? (*):short
Submitted:7/31/2022 11:19:18 CDT
Last modified:8/1/2022 12:37:09 CDT
Database id:134258
Status Flags:TrialDiv
Score (*):48.5812 (normalized score 51.7426)

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 28
Subcategory: "Generalized Fermat"
(archival tag id 227258, tag last modified 2022-10-07 05:37:10)

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_id134258
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"15859176^262144+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 15859176^262144+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 80.83%


15859176^262144+1 is prime! (89478.1223s+0.0197s)
[Elapsed time: 24.86 hours]
modified2022-08-01 12:11:19
created2022-07-31 11:20:01
id180034

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