10072 · 67367000 + 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:10072 · 67367000 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):A11 : Anonymous, Srsieve, CRUS, PRST
Decimal Digits:670174   (log10 is 670173.45570692)
Rank (*):4277 (digit rank is 1)
Entrance Rank (*):3949
Currently on list? (*):yes
Submitted:1/24/2024 13:11:22 UTC
Last modified:1/24/2024 20:37:17 UTC
Database id:136929
Status Flags:none
Score (*):45.4046 (normalized score 1.4708)

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_id136929
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"10072*67^367000+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 10072*67^367000+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Special modular reduction using all-complex AVX-512 FFT length 280K, Pass1=640, Pass2=448, clm=1 on 10072*67^367000+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


10072*67^367000+1 is prime! (3252.0971s+0.0060s)
[Elapsed time: 54.20 minutes]
modified2024-01-24 19:59:44
created2024-01-24 19:05:32
id182767

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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