163 · 778424575 + 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:163 · 778424575 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):A11 : Anonymous, Srsieve, CRUS, PRST
Decimal Digits:1227440   (log10 is 1227439.8745795)
Rank (*):685 (digit rank is 1)
Entrance Rank (*):617
Currently on list? (*):short
Submitted:1/4/2024 11:07:30 UTC
Last modified:1/4/2024 21:37:20 UTC
Database id:136839
Status Flags:none
Score (*):47.2617 (normalized score 9.9213)

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_id136839
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"163*778^424575+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 163*778^424575+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Special modular reduction using zero-padded FMA3 FFT length 672K, Pass1=448, Pass2=1536, clm=4 on 163*778^424575+1
Calling Brillhart-Lehmer-Selfridge with factored part 89.59%


163*778^424575+1 is prime! (17568.3380s+0.0118s)
[Elapsed time: 4.88 hours]
modified2024-01-04 21:15:33
created2024-01-04 16:22:42
id182679

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.