Mill's Constant

Revision as of 01:59, 15 January 2022 by Sap1248 (talk | contribs) (Redefinition to improve clarity)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Mill's Constant is defined as the smallest real number $\theta$ such that $\lfloor\theta^{3^n}\rfloor$ is always a prime number for all natural n.

$\lfloor\theta^{3^n}\rfloor$ is the prime number theorem where $n$ can be any number and $\theta$ is an element from an set of numbers (that may be rational or irrational, and we are not sure) and Mill's Constant is the smallest element in that set. If the Riemann Hypothesis is true, Mill's constant is approximately $1.3063778838630806904686144926...$ and the primes it generates start as $2, 11, 1361, 2521008887, 16022236204009818131831320183,$ $4113101149215104800030529537915953170486139623539759933135949994882770404074832568499, ...$.

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS