On the Density of Primes of the form X^2+c

Abstract

We present a method for finding large fixed-size primes of the form . We study the density of primes on the sets,. We describe an algorithm for generating values of  such that a given prime  is the minimum of the union of prime divisors of all elements in. We also present quadratic forms generating divisors of  and study the prime divisors of its terms. This paper uses the results of Dirichlet's arithmetic progression theorem [1] and the article [6] to rewrite a conjecture of Shanks [2] on the density of primes in . Finally, based on these results, we discuss the heuristics of large primes occurrences in the research set of our algorithm.