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In this article we give a result obtained of an experimental way for the Euler totient function., Comment: 2 pages

In this paper we present the definitions and some properties of several Samrandache Type Functions that are involved in many solved and unsolved problems and conjectures in number theory and recreational mathematics., Comment: 7 pages

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 this article we see that the value takes the Smarandache Function when it is applied to a perfect 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