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evil n.  and  strong prime

First numbers that belong to both sets:

17, 29, 71, 101, 149, 163, 197, 269, 277, 281, 311, 347, 461, 479, 599, 673, 739, 751, 821, 853, 857, 881, 907, 937, 1031, 1049, 1061, 1091, 1117, 1151, 1181, 1229, 1277, 1289, 1297, 1319, 1399, 1427, 1481, 1487, 1523, 1579, 1607, 1619, 1733, 1823, 1847, 1861, 1871, 1901, 1949, 1973, 1997, 2129, 2141, 2203, 2281, 2309, 2333, 2347, 2381, 2389, 2467, 2473, 2539, 2549, 2617, 2671, 2683, 2707, 2729, 2749, 2767, 2797, 2851, 2857, 2897, 2953, 3019, 3167, 3329, 3359, 3389, 3407, 3449, 3461, 3527, 3539, 3557, 3581, 3631, 3671, 3691, 3727, 3917, 3929, 3989, 4049, 4127, 4157, 4211, 4217, 4229, 4241, 4253, 4337, 4349, 4357, 4391, 4441, 4447, 4481, 4517, 4547, 4561, 4583, 4637, 4673, 4721, 4783, 4871, 4931, 4951, 4967, 5009, 5021, 5077, 5147, 5231, 5261, 5273, 5279, 5297, 5407, 5413, 5417, 5431, 5437, 5519, 5527, 5557, 5569, 5623, 5639, 5651, 5657, 5711, 5741, 5849, 5879, 5897, 6007, 6029, 6037, 6089, 6113, 6131, 6143, 6197, 6257, 6269, 6353, 6359, 6389, 6421, 6449, 6469, 6521, 6551, 6599, 6653, 6823, 6827, 6869, 6907, 6997, 7013, 7121, 7127, 7187, 7229, 7237, 7283, 7349, 7451, 7457, 7477, 7487, 7499, 7537, 7547, 7559, 7573, 7589, 7639, 7669, 7723, 7757, 7867, 7877, 7901, 7949, 8009, 8039, 8053, 8081, 8087, 8147, 8353, 8363, 8419, 8443, 8501, 8513, 8537, 8573, 8597, 8623, 8663, 8707, 8731, 8737, 8779, 8803, 8887, 8923, 8929, 9007, 9029, 9041, 9091, 9103, 9127, 9133, 9151, 9173, 9199, 9221, 9239, 9281, 9311, 9341, 9391, 9413, 9431, 9437, 9461, 9491, 9533, 9587, 9629, 9643, 9677, 9689, 9719, 9739, 9787, 9883, 9901, 9941, 9967, 10007, 10037, 10061, 10067, 10133, 10159, 10243, 10267, 10427, 10477, 10589, 10627, 10651, 10663, 10687, 10709, 10723, 10729, 10771.

Some larger examples :