Conjecture no. 3 – “Degree of Factorial”

There are at least “a” primes within the range of n!(a) and n!(a+1), (n,a) being any positive integer greater than 2.

I have to introduce the concept of “degree of Factorial” as I have not been successful in finding any notation for representing a factorial of a factorial, ad. inf.

I define n!(a) as n! of degree a>0.

n!(1) indicates the factorial of degree 1 which is the conventional factorial.

Ex. 5!(1) indicates simply 5! i.e 5*4*3*2*1, i.e 120.

Ex. 5!(2) indicates factorial of 5! i.e (5*4*3*2*1)! or (5!)! or 120!

However, I have not extended this for non positive integer arguments. I welcome our readership to help me extend this via the Gamma function. As always, I invite readers to prove or disprove this conjecture. Thank you for reading this blog.

Nunghead