8 · 105112847 - 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:8 · 105112847 - 1
Verification status (*):Proven
Official Comment (*):Near-repdigit
Proof-code(s): (*):A19 : Propper, Batalov, Srsieve, PRST
Decimal Digits:5112848   (log10 is 5112847.90309)
Rank (*):38 (digit rank is 1)
Entrance Rank (*):38
Currently on list? (*):short
Submitted:1/30/2024 15:05:55 UTC
Last modified:2/7/2024 04:37:17 UTC
Database id:137005
Status Flags:none
Score (*):51.6339 (normalized score 785.7223)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Near-repdigit (archivable *)
Prime on list: yes, rank 1
Subcategory: "Near-repdigit"
(archival tag id 229278, tag last modified 2024-02-07 04:37:20)

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_id137005
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"8*10^5112847-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 8*10^5112847-1 [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 1152K, Pass1=192, Pass2=6K, clm=4 on 8*10^5112847-1
Calling Brillhart-Lehmer-Selfridge with factored part 69.90%


8*10^5112847-1 is prime! (616979.7240s+0.0409s)
[Elapsed time: 7.14 days]
modified2024-02-07 03:40:25
created2024-01-31 00:17:22
id182843

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