# Is there a known mathematical equation to find the nth prime?

I’ve solved for it making a computer program, but was wondering there was a mathematical equation that you could use to solve for the nth prime?

No, there is no known formula that gives the nth prime, except artificial ones you can write that are basically equivalent to “the $n$th prime”. But if you only want an approximation, the $n$th prime is roughly around $n \ln n$ (or more precisely, near the number $m$ such that $m/\ln m = n$) by the prime number theorem. In fact, we have the following asymptotic bound on the $n$th prime $p_n$:

$n \ln n + n(\ln\ln n - 1) < p_n < n \ln n + n \ln \ln n$ for $n\ge{}6$

You can sieve within this range if you want the $n$th prime. [Edit: There are better ideas than a sieve, see the answer by Charles.]

Entirely unrelated: if you want to see formulae that generate a lot of primes (not the $n$th prime) up to some extent, like the famous $f(n)=n^2-n+41$, look at the Wikipedia article formula for primes, or Mathworld for Prime Formulas.