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evil n.  and  weak prime

First numbers that belong to both sets:

3, 23, 43, 83, 89, 113, 139, 293, 317, 337, 349, 353, 359, 383, 389, 401, 449, 467, 503, 509, 523, 547, 571, 619, 643, 683, 691, 773, 797, 811, 839, 863, 887, 983, 1013, 1093, 1097, 1217, 1237, 1283, 1303, 1307, 1381, 1409, 1429, 1433, 1439, 1489, 1499, 1553, 1559, 1601, 1613, 1621, 1637, 1699, 1723, 1811, 1873, 1879, 1889, 1913, 2003, 2039, 2069, 2083, 2089, 2179, 2221, 2239, 2251, 2357, 2393, 2399, 2423, 2593, 2659, 2689, 2699, 2713, 2719, 2791, 2803, 2837, 2909, 2971, 3001, 3049, 3067, 3089, 3137, 3191, 3221, 3259, 3347, 3499, 3533, 3541, 3643, 3677, 3701, 3739, 3769, 3797, 3823, 3863, 3911, 3923, 4003, 4027, 4133, 4177, 4289, 4397, 4423, 4451, 4463, 4493, 4549, 4567, 4651, 4679, 4703, 4733, 4817, 4877, 4889, 4919, 4933, 4937, 4943, 4957, 4973, 5081, 5087, 5153, 5171, 5197, 5209, 5233, 5309, 5351, 5443, 5449, 5479, 5483, 5503, 5507, 5521, 5531, 5581, 5653, 5669, 5693, 5701, 5749, 5783, 5813, 5843, 5861, 5903, 5927, 5939, 5953, 5987, 6011, 6047, 6053, 6133, 6173, 6221, 6229, 6379, 6473, 6481, 6491, 6571, 6581, 6691, 6703, 6737, 6763, 6793, 6829, 6841, 6883, 6917, 6983, 7001, 7109, 7193, 7247, 7433, 7481, 7489, 7507, 7529, 7549, 7577, 7607, 7621, 7643, 7649, 7673, 7703, 7793, 7829, 7937, 8017, 8069, 8093, 8233, 8273, 8329, 8377, 8431, 8543, 8669, 8693, 8719, 8761, 8839, 8863, 8867, 8893, 8941, 8971, 9001, 9067, 9187, 9293, 9403, 9479, 9497, 9521, 9539, 9551, 9623, 9749, 9769, 9859, 9907, 9931, 10069, 10079, 10103, 10181, 10193, 10273, 10303, 10369, 10399, 10429, 10459, 10531, 10613, 10639, 10667, 10753, 10789, 10799, 10861, 10867, 10909, 10957, 10979, 10993, 11003, 11059, 11071, 11093, 11119, 11131, 11161, 11173, 11177, 11243, 11491, 11503, 11597.

Some larger examples :