|Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1|
Durham, North Carolina
Abstract: In 1947 Mills proved that there exists a constant such that is a prime for every positive integer . Determining requires determining an effective Hoheisel type result on the primes in short intervals--though most books ignore this difficulty. 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 does begin with . We calculate this value to decimal places by determining the associated primes to over digits and probable primes (PRPs) to over digits. We also apply the Cramér-Granville Conjecture to Honaker's problem in a related context.
(Concerned with sequences A051021 A051254 and A108739 .)
Received July 14 2005; revised version received August 15 2005. Published in Journal of Integer Sequences August 24 2005.