81 · 22375447 - 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:81 · 22375447 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L3887 : Byerly, PSieve, Rieselprime, LLR
Decimal Digits:715083   (log10 is 715082.70859504)
Rank (*):3906 (digit rank is 1)
Entrance Rank (*):2134
Currently on list? (*):yes
Submitted:11/10/2021 21:35:14 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132922
Status Flags:none
Score (*):45.6038 (normalized score 1.8898)

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_id132922
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"81*2^2375447-1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 81*2^2375447-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 20/2375455 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 81*2^2375447-1 is prime! (6182.4914s+0.0005s) [Elapsed time: 1.72 hours]
modified2022-07-11 18:21:45
created2021-11-10 21:36:01
id178635

Query times: 0.0004 seconds to select prime, 0.0002 seconds to seek comments.
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