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pernicious n.  and  weak prime

First numbers that belong to both sets:

3, 7, 13, 19, 31, 47, 61, 73, 103, 109, 131, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 313, 409, 421, 433, 443, 463, 491, 577, 601, 647, 661, 677, 709, 743, 761, 823, 829, 859, 883, 911, 919, 941, 953, 971, 997, 1033, 1039, 1051, 1063, 1069, 1109, 1129, 1153, 1171, 1193, 1201, 1231, 1259, 1291, 1321, 1327, 1373, 1453, 1459, 1483, 1493, 1571, 1583, 1609, 1627, 1669, 1709, 1831, 1933, 2017, 2099, 2113, 2131, 2143, 2161, 2207, 2213, 2243, 2269, 2273, 2297, 2311, 2341, 2351, 2383, 2441, 2447, 2477, 2621, 2633, 2663, 2693, 2731, 2753, 2777, 2843, 2861, 2887, 2917, 2957, 3041, 3083, 3121, 3169, 3209, 3229, 3253, 3271, 3301, 3331, 3361, 3373, 3413, 3463, 3469, 3529, 3583, 3593, 3617, 3623, 3673, 3779, 3853, 3881, 3889, 3967, 4079, 4093, 4099, 4111, 4129, 4139, 4159, 4219, 4231, 4243, 4261, 4273, 4297, 4339, 4363, 4373, 4483, 4519, 4523, 4639, 4643, 4663, 4723, 4759, 4789, 4793, 4801, 4909, 4969, 5003, 5011, 5059, 5119, 5179, 5237, 5281, 5333, 5399, 5419, 5573, 5641, 5659, 5717, 5827, 6079, 6151, 6199, 6203, 6277, 6287, 6301, 6329, 6343, 6361, 6427, 6451, 6529, 6553, 6661, 6679, 6709, 6803, 6833, 6911, 6949, 6961, 7043, 7159, 7213, 7219, 7253, 7309, 7333, 7369, 7459, 7561, 7691, 8059, 8123, 8171, 8179, 8191, 8221, 8237, 8243, 8293, 8297, 8317, 8369, 8389, 8423, 8467, 8527, 8539, 8581, 8599, 8609, 8629, 8647, 8681, 8741, 8753, 8783, 8807, 8821, 8849, 8933, 9013, 9043, 9049, 9109, 9137, 9161, 9227, 9241, 9257, 9283, 9323, 9349, 9377, 9421, 9433, 9649, 9697, 9743, 9817, 9833, 10009, 10111, 10223, 10247, 10259, 10321, 10333, 10337, 10343, 10433, 10501, 10513, 10567, 10601, 10631, 10691, 10837, 10891, 11261, 11279, 11287.

Some larger examples :