Prime Representing Polynomial with 10 Unknowns - Introduction. Part II

In our previous work [7] we prove that the set of prime numbers is diophantine using the 26-variable polynomial proposed in [4]. In this paper, we focus on the reduction of the number of variables to 10 and it is the smallest variables number known today [5], [10]. Using the Mizar [3], [2] system, we formalize the first step in this direction by proving Theorem 1 [5] formulated as follows: Let k is an element of N. Then k is prime if and only if there exists f, i, j, m, u E N+, r, s, t is an element of N unknowns such that