the nonhypotenuse numbers are those numbers that have no prime factors of the form 4"k"+1. equivalently, any number that cannot be put into the form formula_1 where "k", "m", and "n" are all positive integers, is never a nonhypotenuse number. a number whose prime factors are not of the form 4"k"+1 cannot be the hypotenuse of a primitive triangle, but may still be the hypotenuse of a non-primitive triangle.