restart;

with(NumberTheory):

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

$7$

$2^7-1$

$127$

$\mathrm{isprime}\left(2^7-1\right)$

$\mathrm{true}$

$2^2-1$

$3$

$\mathrm{IsMersenne}\left(2\right)$

$\mathrm{true}$

$2^{11}-1$

$2047$

$\mathrm{IsMersenne}\left(11\right)$

$\mathrm{false}$

$\mathrm{ifactor}\left(2^{11}-1\right)$

$\left(23\right)\left(89\right)$

$\mathrm{interface}\left(\mathrm{rtablesize}=55\right)\:$

$\mathrm{DataSeries}\left(\left[\mathrm{seq}\left(\mathrm{IthMersenne}\left(i\right)\,i=1..52\right)\right]\,\mathrm{labels}=\left[\mathrm{seq}\left(1..52\right)\right]\right)$

Warning, the rankings of the 49th to 52nd Mersenne primes are provisional, since it has not been determined that there do not exist more Mersenne primes between 48th and 52nd

$\left[\begin{array}{cc}1& 2\\ 2& 3\\ 3& 5\\ 4& 7\\ 5& 13\\ 6& 17\\ 7& 19\\ 8& 31\\ 9& 61\\ 10& 89\\ 11& 107\\ 12& 127\\ 13& 521\\ 14& 607\\ 15& 1279\\ 16& 2203\\ 17& 2281\\ 18& 3217\\ 19& 4253\\ 20& 4423\\ 21& 9689\\ 22& 9941\\ 23& 11213\\ 24& 19937\\ 25& 21701\\ 26& 23209\\ 27& 44497\\ 28& 86243\\ 29& 110503\\ 30& 132049\\ 31& 216091\\ 32& 756839\\ 33& 859433\\ 34& 1257787\\ 35& 1398269\\ 36& 2976221\\ 37& 3021377\\ 38& 6972593\\ 39& 13466917\\ 40& 20996011\\ 41& 24036583\\ 42& 25964951\\ 43& 30402457\\ 44& 32582657\\ 45& 37156667\\ 46& 42643801\\ 47& 43112609\\ 48& 57885161\\ 49& 74207281\\ 50& 77232917\\ 51& 82589933\\ 52& 136279841\end{array}\right]$