396101 · 214259638 - 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:396101 · 214259638 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):A20 : Propper, Batalov, Gcwsieve, PRST
Decimal Digits:4292585   (log10 is 4292584.3631159)
Rank (*):60 (digit rank is 1)
Entrance Rank (*):54
Currently on list? (*):short
Submitted:2/3/2024 17:02:31 UTC
Last modified:2/11/2024 07:37:10 UTC
Database id:137129
Status Flags:none
Score (*):51.0985 (normalized score 432.7511)

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 Woodall (archivable *)
Prime on list: yes, rank 4
Subcategory: "Generalized Woodall"
(archival tag id 229300, tag last modified 2024-02-26 15:37:18)

User comments about this prime (disclaimer):

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Ryan Propper writes (3 Feb 2024):  (report abuse)
= 1584404*(512^1584404)-1

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"396101*2^14259638-1" >command_output 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 396101*2^14259638-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FMA3 FFT length 1440K, Pass1=320, Pass2=4608, clm=2 on 396101*2^14259638-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 67/14259658 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using zero-padded FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on 396101*2^14259638-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

396101*2^14259638-1 is prime! (654832.5252s+0.0062s)
[Elapsed time: 7.58 days]
modified2024-02-11 06:56:56
created2024-02-03 17:03:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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