Meh, I feel like 30030 ("30 oh 30"; AKA, "2x3x5x7x11x13") is better, but, that's just me... :P ;) Though 510,510 is honestly pretty cool too... 'Cause it's literally "510 ... 510." (AKA, "2x3x5x7x11x13x17") "30 oh 30" and "510 ... 510" are just pretty nice to say.
Likewise: Primorial [3,408,696] If only because it is the Primorial sieve domain size into which the current largest prime number [24, 862, 048 digits long] falls. Primorial [3,408,695] yields a number that is 24,862,045 digits long, whereas Primorial [3,408,696] yields a number that is 24,862,053 digits long. So, the current longest prime number's length falls between the end of the Primorial [3,408,695] domain and the end of the Primorial [3,408,696] domain. Thank you Mathematica and my new Ryzen 3700X-based desktop for calculating it out for me. My old Phenom II x6 1045T system just wasn't quite up to the task [though it was a decade old]...
Anyway, here's the Mathematica code I used, in case anyone cares. ;) ----- (* Largest known prime: 24,862,048 digits long *) FirstPrime = 1; LastPrime = 3408695; PrimeRange = Range[FirstPrime, LastPrime]; PrimeList = Prime[PrimeRange]; Times @@ PrimeList; IntegerLength[Times @@ PrimeList] [Result:] 24862045 ----- (* Largest known prime: 24,862,048 digits long *) FirstPrime = 1; LastPrime = 3408696; PrimeRange = Range[FirstPrime, LastPrime]; PrimeList = Prime[PrimeRange]; Times @@ PrimeList; IntegerLength[Times @@ PrimeList] [Result:] 24862053 ----- Just something amusing I fiddled with in my spare time. ^_^
Anyway, you'd have to know the first 3,408,695 primes and multiply them together to find out the sieve domain size just to figure out that it's a "candidate," but you'd have to know like all the primes less than or equal to the square root of the number, in order to basically "prove"/check that it's actually prime. Or something? Not entirely sure how they proved it's prime without knowing all the earlier primes [we don't]... Guess they must have some simpler proving method that works on mega-primes? Dunno...
Yes, it is a good number, I suppose. I like the primorials.
Meh, I feel like 30030 ("30 oh 30"; AKA, "2x3x5x7x11x13") is better, but, that's just me... :P ;)
Though 510,510 is honestly pretty cool too... 'Cause it's literally "510 ... 510." (AKA, "2x3x5x7x11x13x17")
"30 oh 30" and "510 ... 510" are just pretty nice to say.
Likewise:
Primorial [3,408,696]
If only because it is the Primorial sieve domain size into which the current largest prime number [24, 862, 048 digits long] falls.
Primorial [3,408,695] yields a number that is 24,862,045 digits long, whereas Primorial [3,408,696] yields a number that is 24,862,053 digits long. So, the current longest prime number's length falls between the end of the Primorial [3,408,695] domain and the end of the Primorial [3,408,696] domain.
Thank you Mathematica and my new Ryzen 3700X-based desktop for calculating it out for me. My old Phenom II x6 1045T system just wasn't quite up to the task [though it was a decade old]...
Anyway, here's the Mathematica code I used, in case anyone cares. ;)
-----
(* Largest known prime: 24,862,048 digits long *)
FirstPrime = 1;
LastPrime = 3408695;
PrimeRange = Range[FirstPrime, LastPrime];
PrimeList = Prime[PrimeRange];
Times @@ PrimeList;
IntegerLength[Times @@ PrimeList]
[Result:] 24862045
-----
(* Largest known prime: 24,862,048 digits long *)
FirstPrime = 1;
LastPrime = 3408696;
PrimeRange = Range[FirstPrime, LastPrime];
PrimeList = Prime[PrimeRange];
Times @@ PrimeList;
IntegerLength[Times @@ PrimeList]
[Result:] 24862053
-----
Just something amusing I fiddled with in my spare time. ^_^
Anyway, you'd have to know the first 3,408,695 primes and multiply them together to find out the sieve domain size just to figure out that it's a "candidate," but you'd have to know like all the primes less than or equal to the square root of the number, in order to basically "prove"/check that it's actually prime. Or something? Not entirely sure how they proved it's prime without knowing all the earlier primes [we don't]... Guess they must have some simpler proving method that works on mega-primes? Dunno...