Recent content by astroultraman

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...