Determining Mills' Constant and a Note on Honaker's Problem

In 1947 Mills proved that there exists a constant A such that bA 3 n c is a prime for every positive integer n. Determining A requires determining an efiective Hoheisel type result on the primes in short intervals|though most books ignore this di‐culty. Under the Riemann Hypothesis, we show that there exists at least one prime between every pair of consecutive cubes and determine (given RH) that the least possible value of Mills’ constant A does begin with 1:3063778838. We calculate this value to 6850 decimal places by determining the associated primes to over 6000 digits and probable < :