31 · 29088085 - 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:31 · 29088085 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):A2 : Propper, Srsieve, PRST
Decimal Digits:2735788   (log10 is 2735787.6795056)
Rank (*):171 (digit rank is 1)
Entrance Rank (*):160
Currently on list? (*):short
Submitted:8/27/2024 14:19:09 UTC
Last modified:8/29/2024 03:37:15 UTC
Database id:138447
Status Flags:none
Score (*):49.7187 (normalized score 103.8225)

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_id138447
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"31*2^9088085-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 31*2^9088085-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FMA3 FFT length 560K, Pass1=448, Pass2=1280, clm=4 on 31*2^9088085-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


31*2^9088085-1 is prime! (133396.6054s+0.0036s)
[Elapsed time: 1.54 days]
modified2024-08-29 03:23:22
created2024-08-27 14:20:02
id184291

Query times: 0.0005 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.