Important: The numtheory package has been deprecated.  Use the superseding commands NumberTheory[IthMersenne], NumberTheory[IsMersenne] instead.

The function mersenne computes Mersenne primes. If the argument n is an integer then mersenne(n) will return $2^n-1$ if $2^n-1$ is known to be prime.  Otherwise, if n is prime, but $2^n-1$ is not determinably prime, then mersenne(n) will return FAIL.  Finally, if n is composite it will return false.

If the argument is a list with one integer element [i], then mersenne([i]) will return the ith Mersenne prime.  If the value is beyond Maple's precomputed list of Mersenne primes, an error will be issued.

The command with(numtheory,mersenne) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{numtheory}\right)\:$

$\mathrm{mersenne}\left(3\right)$

$7$

$\mathrm{mersenne}\left(\left[3\right]\right)$

$31$

$\mathrm{mersenne}\left(4\right)$

$\mathrm{false}$

$\mathrm{mersenne}\left(224737\right)$

$\mathrm{false}$

$\mathrm{mersenne}\left(756853\right)$

$\mathrm{false}$