There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely accurate knowledge of some unknown constant, or effectively require knowledge of the primes ahead of time in order to use the formula. There also exist simple prime-generating polynomials that generate only primes for the first (possibly large) number of integer values. There are also many beautiful formulas involving prime sums and prime products that can be done in closed form.

FRACTRAN | Mills' constant | prime counting function | prime number | prime products | prime sums | Rosser's theorem | sieve | Willans' formula