(263488719 + 1)2 - 2

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:(263488719 + 1)2 - 2
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p432 : Rodermond, Cksieve, OpenPFGW
Decimal Digits:606948   (log10 is 606947.2211083)
Rank (*):4554 (digit rank is 1)
Entrance Rank (*):3991
Currently on list? (*):yes
Submitted:5/18/2023 11:23:19 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:136056
Status Flags:none
Score (*):45.1004 (normalized score 1.2024)

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_id136056
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -tc -q"(2634^88719+1)^2-2" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2634^88719+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 200K, Pass1=640, Pass2=320, clm=1 on A 2016236-bit number
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction AVX-512 FFT length 200K, Pass1=640, Pass2=320, clm=1 on A 2016236-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/2016253 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction AVX-512 FFT length 240K, Pass1=640, Pass2=384, clm=1 on A 2016236-bit number
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction AVX-512 FFT length 200K, Pass1=640, Pass2=320, clm=1 on A 2016236-bit number
Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof)


(2634^88719+1)^2-2 is prime! (32266.2942s+0.0084s)
[Elapsed time: 8.96 hours]
modified2023-05-18 20:21:48
created2023-05-18 11:24:02
id181886

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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