Hardy-Ramanujan Journal |
Referring to a theorem of A. E. Ingham, that for all N≥N0 (an absolute constant), the inequality N3≤p≤(N+1)3 is solvable in a prime p, we point out in this paper that it is implicit that he has actually proved that π(x+h)−π(x)∼h(logx)−1 where h=xc and c(>58) is any constant. Further, we point out that even this stronger form can be proved without using the functional equation of ζ(s).