275 · 22679936 - 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:275 · 22679936 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):A27 : Piesker, PSieve, Srsieve, NPLB, PRST
Decimal Digits:806744   (log10 is 806743.56179244)
Rank (*):3699 (digit rank is 1)
Entrance Rank (*):3687
Currently on list? (*):short
Submitted:10/1/2024 22:54:21 UTC
Last modified:10/2/2024 12:37:15 UTC
Database id:138600
Status Flags:none
Score (*):45.974 (normalized score 2.4469)

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_id138600
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"275*2^2679936-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 275*2^2679936-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FMA3 FFT length 168K, Pass1=896, Pass2=192, clm=2 on 275*2^2679936-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 16532/2679946 ERROR: ROUND OFF 0.46875>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 FMA3 FFT length 192K, Pass1=768, Pass2=256, clm=2 on 275*2^2679936-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


275*2^2679936-1 is prime! (10300.2268s+0.0019s)
[Elapsed time: 2.86 hours]
modified2024-10-02 12:11:30
created2024-10-02 09:19:47
id184444

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