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NumberTheory

 IthMersenne
 Mersenne exponents

 Calling Sequence IthMersenne(i)

Parameters

 i - positive integer

Description

 • The IthMersenne(i) command returns the ith smallest number $n$ such that ${2}^{n}-1$ is known to be prime.
 • If ${2}^{n}-1$ is prime, then it is said to be a Mersenne prime.
 • There are currently 50 known Mersenne primes, but the rankings of the forty-fifth to fiftieth Mersenne primes are provisional, since there might be undiscovered Mersenne primes greater than the forty-fourth but less than the fiftieth.
 • An error will be displayed if i is greater than $50$.

Examples

 > $\mathrm{with}\left(\mathrm{NumberTheory}\right):$
 > $\mathrm{IthMersenne}\left(1\right)$
 ${2}$ (1)
 > $\mathrm{IthMersenne}\left(35\right)$
 ${1398269}$ (2)
 > $\mathrm{IthMersenne}\left(49\right)$
 Warning, the rankings of the 45th to 51st Mersenne primes are provisional, since it has not been determined that there do not exist more Mersenne primes between 44th and 51st
 ${74207281}$ (3)
 > $\mathrm{IthMersenne}\left(52\right)$

Compatibility

 • The NumberTheory[IthMersenne] command was introduced in Maple 2016.