Mills' constant

In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function

${\displaystyle \left\lfloor A^{3^{n}}\right\rfloor }$

is a prime number for all positive natural numbers n. This constant is named after William Harold Mills who proved in 1947 the existence of A based on results of Guido Hoheisel and Albert Ingham on the prime gaps.^[1] Its value is unproven, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... (sequence A051021 in the OEIS).