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evil n.  and  good prime

First numbers that belong to both sets:

5, 17, 29, 53, 71, 101, 149, 257, 269, 311, 347, 593, 599, 739, 821, 853, 937, 1031, 1151, 1277, 1399, 1427, 1847, 1861, 1871, 1973, 1997, 2203, 2333, 2539, 2683, 3167, 3449, 3461, 3527, 3989, 4211, 4217, 4229, 4441, 4447, 4481, 4637, 4783, 4871, 4931, 4967, 5387, 5407, 5413, 5623, 5639, 5651, 6007, 6029, 6037, 6197, 6257, 6263, 6521, 6551, 6653, 6823, 7451, 7457, 7477, 7523, 7537, 8039, 8053, 8081, 8087, 8501, 8513, 8597, 8623, 8663, 9103, 9127, 9133, 9151, 9311, 9391, 9413, 10007, 10037, 10061, 10067, 10133, 10589, 10831, 11047, 11239, 11887, 12373, 12377, 13669, 13679, 13687, 14293, 14321, 15013, 15073, 15259, 16823, 16829, 16871, 16979, 17837, 17881, 17903, 18899, 18911, 19421, 19889, 19913, 19961, 20681, 20717, 20743, 20873, 20897, 21313, 21377, 21467, 21491, 22541, 22619, 22637, 22961, 23003, 23537, 23549, 23557, 23741, 24763, 25147, 25301, 25913, 27427, 27733, 27737, 28277, 28387, 28493, 28591, 29983, 30011, 30059, 30089, 30491, 30671, 30803, 31121, 31147, 31957, 32027, 32051, 32057, 35747, 36451, 36527, 38149, 38167, 38177, 38669, 39079, 40459, 40483, 41011, 41113, 41507, 41513, 41579, 41593, 41603, 41887, 41947, 43573, 43577, 43933, 43943, 43961, 44449, 44491, 45817, 46133, 46439, 47119, 47269, 47279, 47287, 47293, 47491, 47497, 48299, 48407, 48473, 48479, 48751, 48989, 50741, 51197, 51413, 52501, 52511, 52529, 52541, 54269, 54311, 54347, 54361, 54367, 54401, 55619, 55661, 55763, 55793, 56369, 56437, 60589, 60601, 60607, 61253, 61463, 61469, 63299, 63311, 64577, 64601, 64849, 64871, 64877, 64997, 65537, 66293, 66359, 66449, 66841, 66851, 66919, 67033, 67121, 69677, 69737, 69761, 69809, 69821, 69827, 69991, 69997, 70099, 70111, 70117, 70823, 70841, 71143, 71233, 73277, 73303, 73361, 73517, 73523, 73547, 75133, 75149, 75161, 75167, 76463, 77137, 77237, 77261, 79031, 79103, 79531, 79601, 79757, 79769, 79811, 80141.

Some larger examples :