An Exact Formula for the Primes: Willans' Formula

I think this currently is a mathematical curiosity, but you never know whether it might lead to a better understanding of the prime numbers, a faster factorization algorithm, or whatever.

An IMO more interesting curiosity is Mill’s constant “the smallest positive real number A such that the floor function of the double exponential function ⌊A^3^n⌋ is a prime number for all natural numbers n” (https://en.wikipedia.org/wiki/Mills%27_constant)

(I think it’s more interesting because of the simplicity of the formula. On the negative side, it doesn’t generate all primes)

(https://www.wikiwand.com/en/Formula_for_primes has more curious formulas)