 This particular polynomial is related to Euler's prime-generating polynomial "x"2 − "x" + 41 by replacing "x" with 2"x", or equivalently, by restricting "x" to the even numbers.The constant "A" is given by a product running over all prime numbers,

in which formula_8 is number of zeros of the quadratic polynomial modulo "p" and therefore takes one of the values 0, 1, or 2.Hardy and Littlewood break the product into three factors as

Here the factor ε, corresponding to the prime 2, is 1 if "a" + "b" is odd and 2 if "a" + "b" is even.