On a recursive formula for the sequence of primes and applications to the twin prime problem
In this paper we give a recursive formula for the sequence of primes and apply it to find a necessary and sufficient condition in order that a prime number is equal to . Applications of previous results are given to evaluate the probability that is of the form ; moreover we prove that the limit of this probability is equal to zero as goes to . Finally, for every prime we construct a sequence whose terms that are in the interval are the first terms of two twin primes. This result and...