Let's define δ(n) = ( q≤n 1 q − log log n − B), where B ≈ 0.2614972128 is the Meissel-Mertens constant. The Robin theorem states that δ(n) changes sign infinitely often. We prove if the inequality δ(p) ≤ 0 holds for a prime p big enough, then the Riemann Hypothesis should be false. However, we could restate the Mertens second theorem as limn→∞ δ(pn) = 0 where pn is the n th prime number. In this way, this work could mean a new step forward in the direction for finally solving the Riemann Hypothesis.