An approximate function for counting the primes between n^2 and (n+1)^2 and some approximations for irrational numbers and trigonometric functions.

x/ln(n) – log(n) counts the primes between n^2 and (n+1)^2 fairly well.

Here the x represents the difference between (n+1)^2 and n^2.

The log in this case is considered to be a log to the base pi.

It would be appreciated if someone could find a better approximating function.

Some Approximations

233/144 is a good approximation for the Golden Ratio i.e 1/2(1+sqrt(5)

Sin(90)=96184079/107611350.

Here the Sin(90) is interpreted in radians.

Thank you

Nunghead