5003 · 21914141 + 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:5003 · 21914141 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L5724 : Pilz, LLR2, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:576218   (log10 is 576217.55616075)
Rank (*):5541 (digit rank is 1)
Entrance Rank (*):4886
Currently on list? (*):no
Submitted:2/25/2024 17:24:08 UTC
Last modified:2/25/2024 18:37:09 UTC
Removed (*):3/1/2024 13:15:37 UTC
Database id:137613
Status Flags:none
Score (*):44.9408 (normalized score 0.9162)

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.
machineUsing: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"5003*2^1914141+1" >command_output 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 5003*2^1914141+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3
Special modular reduction using all-complex FMA3 FFT length 144K, Pass1=768, Pass2=192, clm=2 on 5003*2^1914141+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

5003*2^1914141+1 is prime! (1771.9417s+0.0005s)
[Elapsed time: 29.60 minutes]
modified2024-02-25 17:54:37
created2024-02-25 17:25:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.