where "b" and "c" are integer constants. When "b" is even, the lines are diagonal, and either all numbers are odd, or all are even, depending on the value of "c". It is therefore no surprise that all primes other than 2 lie in alternate diagonals of the Ulam spiral. Some polynomials, such as formula_2, while producing only odd values, factorize over the integers formula_3 and are therefore never prime except possibly when one of the factors equals 1. Such examples correspond to diagonals that are devoid of primes or nearly so.