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Chen prime  and  weak prime

First numbers that belong to both sets:

3, 7, 13, 19, 23, 31, 47, 83, 89, 109, 113, 131, 139, 167, 181, 199, 233, 293, 317, 337, 353, 359, 389, 401, 409, 443, 449, 467, 491, 503, 509, 571, 577, 647, 677, 683, 743, 761, 797, 811, 829, 839, 863, 887, 911, 919, 941, 953, 971, 983, 1039, 1097, 1109, 1193, 1201, 1217, 1259, 1283, 1291, 1327, 1381, 1409, 1439, 1459, 1499, 1553, 1559, 1583, 1601, 1621, 1637, 1669, 1709, 1759, 1889, 1913, 1979, 2003, 2017, 2029, 2039, 2069, 2099, 2179, 2207, 2213, 2243, 2251, 2269, 2351, 2357, 2393, 2441, 2447, 2477, 2543, 2557, 2621, 2659, 2699, 2719, 2731, 2777, 2837, 2843, 2861, 2909, 2927, 2939, 2957, 2971, 3041, 3083, 3089, 3137, 3191, 3221, 3259, 3271, 3347, 3413, 3541, 3559, 3593, 3677, 3709, 3779, 3797, 3803, 3863, 3881, 3889, 3919, 3947, 4007, 4099, 4133, 4139, 4289, 4297, 4339, 4397, 4451, 4567, 4643, 4679, 4703, 4733, 4789, 4801, 4817, 4889, 4909, 4937, 4969, 5087, 5153, 5171, 5197, 5309, 5351, 5399, 5483, 5507, 5531, 5581, 5669, 5701, 5791, 5813, 5851, 5903, 5939, 5987, 6011, 6047, 6079, 6101, 6287, 6329, 6427, 6481, 6491, 6581, 6607, 6619, 6661, 6709, 6737, 6803, 6833, 6841, 6911, 6971, 7001, 7043, 7079, 7109, 7129, 7193, 7247, 7253, 7309, 7417, 7433, 7481, 7507, 7529, 7541, 7561, 7591, 7607, 7649, 7727, 7793, 7829, 7853, 7907, 7937, 8011, 8059, 8069, 8093, 8171, 8191, 8221, 8297, 8329, 8369, 8389, 8527, 8543, 8581, 8609, 8681, 8741, 8807, 8849, 8933, 8951, 9001, 9067, 9109, 9209, 9227, 9257, 9377, 9467, 9479, 9521, 9551, 9649, 9661, 9743, 9769, 9791, 9839, 10039, 10079, 10111, 10169, 10181, 10193, 10247, 10259, 10343, 10369, 10399, 10433, 10487, 10531, 10601, 10639, 10667, 10711, 10739, 10799, 10837, 10867, 10891.

Some larger examples :