983 · 22164206 - 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:983 · 22164206 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p435 : Dettweiler, LLR2, PSieve, Srsieve, NPLB, OpenPFGW
Decimal Digits:651494   (log10 is 651493.91534948)
Rank (*):4386 (digit rank is 1)
Entrance Rank (*):4266
Currently on list? (*):yes
Submitted:3/13/2024 00:09:43 UTC
Last modified:3/13/2024 02:37:12 UTC
Database id:137803
Status Flags:none
Score (*):45.3178 (normalized score 1.3649)

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_id137803
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"983*2^2164206-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 983*2^2164206-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using AVX-512 FFT length 144K, Pass1=192, Pass2=768, clm=1 on 983*2^2164206-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 57688/2164217 ERROR: ROUND OFF 0.47014>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 AVX-512 FFT length 192K, Pass1=192, Pass2=1K, clm=1 on 983*2^2164206-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


983*2^2164206-1 is prime! (6360.0215s+0.0008s)
[Elapsed time: 1.77 hours]
modified2024-03-13 02:22:44
created2024-03-13 00:36:40
id183645

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