An Amazing Prime Heuristic

Abstract: Dickson conjectured that a set of polynomials will take on infinitely many simultaneous prime values. Later others, such as Hardy and Littlewood, gave estimates for the number of these primes. In this article we look at this conjecture, develop a simple heuristic and rederive these classic estimates. We then apply them to several special forms of primes and compare the estimates with the actual numbers.