In mathematics, it is known that there exist real positive numbers θ such that the integer part of
is a prime number, for all positive integers n. The least such number is called Mills' constant and is approximately
- 1.30637788386308069046...
It is hard to calculate Mills' constant accurately (although several thousand digits are known), because to do that with the current state of knowledge one needs to know the primes it generates. There is no formula for this number as of now, and it is not even known if this number is rational. It is known, however, that the first few primes generated are 2, 11, 1361, 2521008887...
This constant is named after W. H. Mills who proved in 1947 the existence of θ based on results of Hoheisel and Ingham on the gaps between the primes.