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Chen prime  and  good prime

First numbers that belong to both sets:

5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 101, 127, 149, 179, 191, 227, 251, 257, 269, 307, 311, 347, 419, 431, 541, 557, 563, 569, 587, 599, 641, 809, 821, 937, 1009, 1031, 1151, 1277, 1367, 1399, 1427, 1847, 1871, 1997, 2237, 2267, 2333, 2339, 2531, 2609, 2647, 2657, 2687, 2999, 3167, 3251, 3299, 3457, 3461, 3511, 3527, 3821, 3847, 3907, 3989, 4001, 4211, 4217, 4229, 4441, 4447, 4481, 4637, 4861, 4871, 4931, 4967, 5381, 5387, 5639, 5651, 6007, 6029, 6197, 6257, 6521, 6551, 6637, 6659, 6689, 6761, 6779, 6947, 7451, 7457, 7517, 8081, 8087, 8219, 8501, 8597, 8663, 8689, 8999, 9311, 10007, 10037, 10061, 10067, 10091, 10133, 10597, 10847, 11057, 11657, 11699, 11777, 11897, 12197, 12227, 12239, 12377, 12889, 13679, 14321, 14369, 14387, 14401, 14519, 14699, 15053, 15227, 15259, 15269, 16411, 16829, 16871, 16979, 17291, 17783, 17837, 17903, 17909, 18899, 18911, 19001, 19139, 19379, 19417, 19421, 19889, 19961, 20717, 20849, 20897, 20981, 21377, 21467, 21491, 21557, 22541, 22613, 22619, 22637, 22691, 22697, 22961, 23531, 23537, 23549, 23557, 23741, 24917, 25087, 25301, 25537, 25561, 25577, 26669, 26681, 27397, 27407, 27611, 27689, 27737, 28277, 28387, 28571, 28597, 30011, 30059, 30089, 30491, 30631, 30671, 30757, 31121, 32027, 32057, 32297, 32969, 33287, 33311, 33329, 35729, 35747, 35797, 35801, 35831, 35951, 35963, 36467, 36527, 38177, 38557, 38651, 38669, 40427, 40459, 40697, 40739, 40751, 41131, 41141, 41177, 41579, 41843, 41849, 41887, 43577, 43889, 43961, 44491, 46049, 46091, 46133, 46399, 46439, 47051, 47111, 47279, 48299, 48311, 48407, 48479, 48731, 48757, 48989, 51131, 51197, 51329, 51341, 51407, 51419, 52511, 52529, 52541, 53591, 54251, 54269, 54311, 54361, 54401, 55619, 55661, 55787, 55793, 56359, 56369, 56377, 60601, 61211, 61253, 61331, 61469, 62459, 63299, 63311, 64553, 64567.

Some larger examples :