In this paper I make the following three conjectures: (I) there exist an infinity of primes p obtained concatenating even numbers n with 0 then with n + 2, then again with 0, then with n + 5 (example: for n = 44, the number p = 44046049 is prime). It is notable that are found chains with 4 primes p obtained for 4 consecutive even numbers n (example: 17201740177, 17401760177, 17601780181, 17801800183, obtained for 172, 174, 176, 178); (II) there exist an infinity of pairs of primes (p, q) obtained applying on two consecutive even numbers (m, n) the method of concatenation showed in the conjecture above (note that q – p = 20202; 2002002; 200020002 and so on); (III) there exist, for any k positive integer, an infinity of primes q = p + n, where p is prime and n is the number obtained concatenating 2 with a number of k digits of 0 then with 2 then again with the same number of k digits of 0 then again with 2.