>>>Let p and q be successive primes.Andrica conjectures that
q - p < sqrt(q) + sqrt(p)
whereas Tschebysheff proved merely that
q - p < p
which is far weaker.<<<
Andrica's conjecture doesn't seem very tight compared to the two:
x^2 < p < (x+1)^2
x^2 < p < x^2 + x
Andrica's conjecture looks comparable to the first one.
Can it be tightened?