204 · 532454080 - 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:204 · 532454080 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L5410 : Anonymous, Srsieve, CRUS, LLR
Decimal Digits:1237785   (log10 is 1237784.2636227)
Rank (*):668 (digit rank is 1)
Entrance Rank (*):456
Currently on list? (*):short
Submitted:4/10/2023 07:26:15 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:135931
Status Flags:none
Score (*):47.2874 (normalized score 10.18)

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_id135931
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -tp -q"204*532^454080-1" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 204*532^454080-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 480K, Pass1=960, Pass2=512, clm=1 on 204*532^454080-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 36/4111832 ERROR: ROUND OFF 0.4523>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 504K, Pass1=1344, Pass2=384, clm=1 on 204*532^454080-1
Calling Brillhart-Lehmer-Selfridge with factored part 46.91%


204*532^454080-1 is prime! (57013.7845s+0.0145s)
[Elapsed time: 15.84 hours]
modified2023-04-10 23:17:16
created2023-04-10 07:27:01
id181745

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