 This conjecture, which Hardy and Littlewood called "Conjecture F", is a special case of the Bateman–Horn conjecture and asserts an asymptotic formula for the number of primes of the form "ax"2 + "bx" + "c".Rays emanating from the central region of the Ulam spiral making angles of 45° with the horizontal and vertical correspond to numbers of the form 4"x"2 + "bx" + "c" with "b" even; horizontal and vertical rays correspond to numbers of the same form with "b" odd.Conjecture F provides a formula that can be used to estimate the density of primes along such rays.