The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, … (sequence A000043 in the OEIS) and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, … (sequence A000668 in the OEIS).
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