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evil n.  and  prime n.

First numbers that belong to both sets:

3, 5, 17, 23, 29, 43, 53, 71, 83, 89, 101, 113, 139, 149, 163, 197, 257, 263, 269, 277, 281, 293, 311, 317, 337, 347, 349, 353, 359, 373, 383, 389, 401, 449, 461, 467, 479, 503, 509, 523, 547, 571, 593, 599, 619, 643, 673, 683, 691, 739, 751, 773, 797, 811, 821, 839, 853, 857, 863, 881, 887, 907, 937, 977, 983, 1013, 1031, 1049, 1061, 1091, 1093, 1097, 1103, 1117, 1151, 1181, 1217, 1223, 1229, 1237, 1277, 1283, 1289, 1297, 1303, 1307, 1319, 1381, 1399, 1409, 1427, 1429, 1433, 1439, 1481, 1487, 1489, 1499, 1511, 1523, 1553, 1559, 1579, 1601, 1607, 1613, 1619, 1621, 1637, 1699, 1723, 1733, 1811, 1823, 1847, 1861, 1871, 1873, 1879, 1889, 1901, 1907, 1913, 1949, 1973, 1997, 2003, 2039, 2069, 2083, 2089, 2129, 2141, 2179, 2203, 2221, 2239, 2251, 2281, 2287, 2309, 2333, 2347, 2357, 2381, 2389, 2393, 2399, 2417, 2423, 2467, 2473, 2539, 2549, 2593, 2617, 2659, 2671, 2683, 2689, 2699, 2707, 2713, 2719, 2729, 2749, 2767, 2791, 2797, 2803, 2837, 2851, 2857, 2897, 2903, 2909, 2953, 2971, 3001, 3019, 3049, 3067, 3089, 3137, 3167, 3191, 3221, 3259, 3307, 3329, 3347, 3359, 3389, 3407, 3449, 3461, 3499, 3527, 3533, 3539, 3541, 3557, 3581, 3631, 3643, 3671, 3677, 3691, 3701, 3727, 3739, 3769, 3797, 3823, 3863, 3911, 3917, 3923, 3929, 3989, 4003, 4027, 4049, 4127, 4133, 4157, 4177, 4211, 4217, 4229, 4241, 4253, 4289, 4337, 4349, 4357, 4391, 4397, 4409, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4493, 4517, 4547, 4549, 4561, 4567, 4583, 4597, 4637, 4651, 4673, 4679, 4691, 4703, 4721, 4733, 4783, 4817, 4871, 4877, 4889, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4973, 5009, 5021, 5077, 5081.

Some larger examples :