I tried but it keeps running without giving me any output:
Pr := (x = 2^n - 1;
y = x;
a = ((x + y/2 + x - y - 1)/(x - y - 1)) - ((x + y))/(x + y)/2;
r = IntegerPart[a];
g1 = Mod[r, 9961];
g2 = {28, 167, 210, 237, 245, 412, 545, 636, 671, 693, 833, 875,
910, 917, 980, 1014, 1029, 1098, 1351, 1358, 1372, 1413, 1420,
1448, 1526, 1665, 1680, 1792, 1834, 1925, 2029, 2184, 2240, 2260,
2338, 2400, 2401, 2443, 2534, 2590, 2681, 2771, 2891, 2912,
2925, 3016, 3023, 3030, 3199, 3255, 3283, 3597, 3758, 3759, 3863,
3884, 3920, 3927, 3976, 4011, 4137, 4165, 4200, 4228, 4270,
4333, 4438, 4459, 4501, 4550, 4570, 4613, 4641, 4738, 4760, 4788,
4830, 4844, 4865, 4871, 4900, 4907, 4983, 5004, 5088, 5117,
5333, 5334, 5389, 5467, 5544, 5586, 5859, 5894, 5922, 5949, 6061,
6104, 6132, 6209, 6230, 6313, 6348, 6377, 6467, 6566, 6573,
6600, 6706, 6720, 6740, 6853, 6874, 6887, 6951, 6978, 6986, 7083,
7084, 7090, 7097, 7202, 7216, 7224, 7308, 7552, 7608, 7728,
7770, 7840, 7854, 7917, 7937, 7952, 8028, 8183, 8231, 8280, 8323,
8344, 8357, 8469, 8539, 8568, 8645, 8715, 8722, 8742, 8820,
8903, 8988, 9029, 9030, 9057, 9106, 9135, 9155, 9289, 9386, 9401,
9485, 9555, 9659, 9918, 9960});
n; While[True, If[g1 = g2, Print[x]]; n++]