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In this article we gave a recurrence to obtain the n-th prime number as function of the (n-1)-th prime number., Comment: 3 pages

In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a corollary to an algebraic identity., Comment: 6 pages

Formula for the nth prime using elementary arithmetical functions based in a previous formula changing the characteristic function of prime numbers., Comment: 3 pages

Using inequalities of Rosser and Schoenfeld, we prove formulas for pi(n) and the n-th prime that involve only the elementary operations +,-,/ on integers, together with the floor function. Pascal Sebah has pointed out that the formula for pi(n) operates in O(n^(3/2)) time. Similar formulas were proven using Bertrand's Postulate by Stephen Regimbal, An explicit formula for the k-th prime number, Mathematics Magazine, 48 (1975), 230-23, Comment: 4 pages; similar formulas were proven using Bertrand's Postulate by S. Regimbal, An explicit formula for the k-th prime number, Math. Mag., 48 (1975), 230-232