Prime Representing Polynomial

Summary The main purpose of formalization is to prove that the set prime numbers diophantine, i.e., representable by a polynomial formula. We formalize this problem, using Mizar system [1], [2], in two independent ways, proving existence without formulating it explicitly as well with its indication. First, we reuse nearly all techniques invented MRDP-theorem [11]. Applying trick schemes go beyond first-order logic give short sophisticated proof for such but explicitly. Then formulate proposed [6] has 26 variables language follows ( w · z + h j − q ) 2 +(( g k )·( )+ +(2 3 ·(2· +2)·( n 1) +1− f p e 2) 1 o x −′ y (16 r u ((( )) 4 d c m l i v b (2 s t and any positive integer so necessary sufficient there exist other natural - which equals zero. not best known result relation numbers, since diophantine equation over ℕ can be reduced one 13 unknowns [8] or even less [5], [13]. currently where constructed 10 [7] 7 case Fermat Mersenne number [4]. are focusing our efforts direction.