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evil n.  and  twin primes

First numbers that belong to both sets:

3, 5, 17, 29, 43, 71, 101, 139, 149, 197, 269, 281, 311, 347, 349, 461, 523, 571, 599, 619, 643, 811, 821, 857, 881, 1031, 1049, 1061, 1091, 1093, 1151, 1229, 1277, 1289, 1303, 1319, 1427, 1429, 1481, 1487, 1489, 1607, 1619, 1621, 1699, 1723, 1871, 1873, 1879, 1949, 1997, 2083, 2089, 2129, 2141, 2239, 2309, 2381, 2549, 2593, 2659, 2689, 2713, 2729, 2791, 2803, 2971, 3001, 3167, 3259, 3329, 3359, 3389, 3461, 3527, 3539, 3541, 3557, 3581, 3671, 3769, 3823, 3917, 3929, 4003, 4049, 4127, 4157, 4217, 4229, 4241, 4337, 4423, 4481, 4517, 4547, 4549, 4637, 4651, 4721, 4931, 4933, 4967, 5009, 5021, 5231, 5233, 5279, 5417, 5443, 5479, 5503, 5519, 5521, 5639, 5651, 5653, 5657, 5741, 5849, 5879, 6089, 6131, 6133, 6197, 6269, 6359, 6449, 6551, 6571, 6691, 6703, 6763, 6793, 6827, 6829, 6869, 7127, 7349, 7457, 7487, 7489, 7547, 7549, 7559, 7589, 7757, 7877, 7949, 8009, 8087, 8233, 8431, 8537, 8597, 8839, 8863, 8971, 9001, 9041, 9239, 9281, 9341, 9431, 9437, 9461, 9629, 9677, 9719, 9769, 9859, 9931, 10007, 10037, 10067, 10069, 10273, 10303, 10427, 10429, 10459, 10531, 10709, 10859, 10861, 10889, 10937, 11059, 11071, 11119, 11161, 11171, 11173, 11351, 11491, 11549, 11717, 11779, 11833, 11939, 11941, 11971, 12043, 12073, 12163, 12377, 12611, 12613, 12821, 12917, 13003, 13219, 13337, 13399, 13679, 13681, 13691, 13693, 13709, 13721, 13757, 13829, 13877, 13901, 13999, 14011, 14081, 14251, 14321, 14549, 14563, 15139, 15271, 15289, 15331, 15581, 15641, 15647, 15731, 15733, 15737, 16063, 16229, 16363, 16451, 16453, 16631, 16649, 16691, 16693, 16829, 16901, 16979, 16981, 17189, 17207, 17417, 17491, 17597, 17657, 17683, 17791, 17837, 17911, 17921, 17957, 17987, 17989, 18041, 18047, 18119, 18131, 18133, 18251, 18253, 18287, 18289, 18311, 18521, 18911.

Some larger examples :