How can tell if there is a prime number between any two numbers? Is there a conjecture, statement, formula or anything that determines whether or not there is a prime between two numbers? I'm not looking for a computer algorithm. Any help would be appreciated.
I highly doubt this is possible. Otherwise you could simply check any number of being prime, just by considering the number itself and the number +1 or something along these lines. But checking numbers being prime is hard...
The best we can do is that for any $x \ge 89693$ there is always at least one prime between $x$ and $x + \dfrac{1}{\log^3 x}$. This is much stronger than Bertrand's postulate and was proved by Pierre Dusart.