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A Mersenne prime is in the form of \(2^S-1\). Known Mersenne prime numbers are \(2^{3}-1\), \(2^{5}-1\), \(2^{7}-1\), \(2^{13}-1\), \(2^{17}-1\), \(2^{19}-1\), \(2^{31}-1\), \(2^{61}-1\), \(2^{89}-1\), \(2^{107}-1\) and \(2^{127}-1\). Overall Mersenne primes are efficient in their implementation.