For all integers n if n greater than 2 then there exists prime number p such that n less than p less than n factorial What is the proof?

The proof relies on a result from number theory known as the Bertrand's postulate, which states that for any integer ( n > 1 ), there exists at least one prime ( p ) such that ( n < p < 2n ). Since ( n! ) (n factorial) grows much faster than ( 2n ) for ( n > 2 ), we can conclude that there are primes not only between ( n ) and ( 2n ) but also between ( n ) and ( n! ). Thus, for any integer ( n > 2 ), there exists a prime ( p ) such that ( n < p < n! ).