Cubic and Consecutive Concern (Posted on 2010-03-11)

Determine the probability that for a base ten positive integer N drawn at random between 2 and 101 inclusively, the number N^{3} + 1 is expressible in the form p*q*r, where p, q, r are three distinct positive integers such that p, q and r (in this order) corresponds to three consecutive terms of an arithmetic sequence.