In sieve method, we could get the prime numbers between p and p^2 applying the primes less than prime number p. Is there any conclusion about the gap of these primes? Some conjectures show the upper bound of primes gaps before p is g(p)< ln(p)^2 or g(p)<p^(1/2) (If RH is true). But here we just consider the primes between p and p^2, which are filtered by determinate primes. So I want to know whether we could get some easy conclusions about their gaps by elementary number theory. For example, could we prove the gap of the primes between p and p^2 is less than p? My calculation shows it’s true.