Phi(3, - 4658591048576)
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:||Phi(3, - 4658591048576)|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized unique|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L4561 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR|
|Decimal Digits:||11887192 (log10 is 11887191.240435)|
|Rank (*):||8 (digit rank is 1)|
|Entrance Rank (*):||7|
|Currently on list? (*):||short|
|Submitted:||5/31/2023 19:32:31 UTC|
|Last modified:||7/25/2023 13:37:29 UTC|
|Score (*):||54.2155 (normalized score 12157.3677)|
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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.
field value prime_id 136107 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"Phi(3,-465859^1048576)" 2>&1
PFGW Version 18.104.22.168BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3,-465859^1048576) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Generic modular reduction using generic reduction AVX-512 FFT length 4200K, Pass1=1920, Pass2=2240, clm=1 on A 39488395-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 50.00%
Phi(3,-465859^1048576) is prime! (4730339.7767s+1.8951s)
[Elapsed time: 54.75 days]
modified 2023-07-25 13:32:04 created 2023-05-31 19:33:01 id 181937