with the series representation of sin or cos as a starting point (you don't know nothing else about those functions), how to prove:
a. they are periodic.
b. the value of the period.
yea man you are right thanks, i forgot to think about the case where the square is between the consecutive primes and using only my previous reasoning i can only conclude that qrt(p3)-sqrt(p2)<2. In order to work the Strong Legendre should read something like this: there is always a prime...
i think we can agree that a stronger legendre's conjecture (there is at least 2 primes between consecutive squares) implies andrica's easily.
proof:
if k^2 < pn < p(n+1) <(k+1)^2 than applying sqrt
k< sqrt(pn) < sqrt(p(n+1)) < k+1
the smaller interval must fit in the bigger one so...