  This note presents a result on the maximal prime gap of the form p_(n+1) -
p_n <= C(log p_n)^(1+e), where C > 0 is a constant, for any arbitrarily small
real number e > 0, and all sufficiently large integer n > n_0. Equivalently,
the result shows that any short interval [x, x + y], y => C(log x)^(1+e),
contains prime numbers for all sufficiently large real numbers x => x_0
unconditionally. An application demonstrates that a prime p => x > 2 can be
determined in deterministic polynomial time O(log(x)^8).
