A number field F is called p-rational for an odd prime p, if the Galois group of the maximal pro-p extension of F that is unramified outside p is pro-p free. It was introduced by Abbas Movahhedi to find non-abelian number fields for which the Leopoldt conjecture at p is true. In this talk, we briefly explain the theory of p-rationality. We also show that if l is a Sophie Germain prime such that p is a primitive root modulo l, then Q(\zeta_{2l+1})^{+} is p-rational if p is less than 4l. We also give a heuristic evidence for the recent conjecture of Georges Gras that a number field is p-rational for all but finitely many primes p.