In the framework of our research in the number theory, we discovered with the computing assistance of Phillipe Alsina, Pierre Gazzano and André Solaris and proved that the number Lehmer -Ramanujan τ(331^2129-1) is a prime number of 29.492 digits. We used the method of elliptic curves with 32 core computer. This prime number is the first gigantic, since it has more than 10.000 digits. It is the thirteenth gigantic number that we discovered. The other twelve have 11.002, 13.441, 14.703, 15.515, 15.834, 16.386, 16.526, 18.626, 19.900, 22.506, 23.770 and 26.643 digits. In total we have 64 prime numbers Lehmer -Ramanujan, which proves in practice the efficiency of our methodology for the discovery of large prime numbers that don’t have the form of Mersenne. This step is the implementation of our theoretic approach.