Conjecture no. 5: A further extension of Legendre’s conjecture to different powers.

There is at least one prime in the interval n^a to (n+1)^b, given that,
i) n, a, b are positive integers greater than 1 and cannot have the same value.
ii) a and b are relatively prime; i.e., GCD of (a,b) =1… at least 1 prime exists in this interval.
However, if a and b are not relatively prime, i.e GCD of (a,b) /= 1 then the GCD of the two powers (a,b) results in there being at least greater than 1 amount of primes in the interval.