As the internet evolves and computer networks become accessible, most business transactions are done over the internet. Potential threat to the information is always present and attempts are being made to provide maximum security over the network. One of such new techniques is using multiple prime numbers for RSA cryptosystem, which is not easily breakable. Also, typical prime numbers are used in order to strengthen the algorithm to ensure safe data exchange. In this paper, we used three Mersenne prime numbers to construct a new RSA cryptosystem which provides more efficiency and reliability over the network. Mathematics Subject Classification (2010): 11T71, 14G50, 68P25, 94A60.