  Assuming the Riemann hypothesis, this article discusses a new elementary
argument that seems to prove that the maximal prime gap of a finite sequence of
primes p_1, p_2, ..., p_n <= x, satisfies max {p_(n+1) - p_n : p_n <= x} <=
c1((logx)^2)/loglogx, c1 > 0 constant. Equivalently, it shows that the very
short intervals (x, x + y] contain prime numbers for all y >
c2((logx)^2)/loglogx, c2 > 0 constant, and sufficiently large x > 0.
