TITLE: Strong Bertrand postulate
QUESTION [7 upvotes]: Is it known that for every epsilon there is N_0 such that all intervals of the form [N, (1+\epsilon)*N], where N > N_0, contain prime numbers?

REPLY [8 votes]: If one wants an explicit bound on N0, apparently this can be gleaned from a Ph.D. thesis by Pierre Dusart (in French) which contains the result that for all x > 3275 there is a prime between x and x(1 + 1/(2 ln2 x)). So we can take N0 to be max(3275,exp((2 epsilon)−1/2)).