Abstract
The number 2 110503 − 1 {2^{110503}} - 1 is a Mersenne prime. There are exactly two Mersenne exponents between 100000 and 139268, and there are no Mersenne exponents between 216092 and 353620. Thus, the number 2 132049 − 1 {2^{132049}} - 1 has been verified as the 30th Mersenne prime in order of size.
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