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pernicious n.  and  strong prime

First numbers that belong to both sets:

11, 17, 37, 41, 59, 67, 79, 97, 107, 127, 137, 179, 191, 223, 227, 239, 251, 307, 331, 367, 379, 397, 419, 431, 439, 457, 487, 499, 521, 541, 557, 569, 587, 613, 617, 631, 641, 659, 701, 719, 727, 757, 769, 787, 809, 827, 877, 929, 967, 1009, 1087, 1163, 1213, 1249, 1301, 1361, 1423, 1447, 1451, 1543, 1549, 1567, 1597, 1657, 1667, 1693, 1697, 1721, 1741, 1777, 1801, 1867, 1877, 1931, 1987, 1993, 2053, 2063, 2081, 2087, 2111, 2137, 2153, 2237, 2267, 2293, 2339, 2371, 2377, 2411, 2437, 2459, 2503, 2521, 2531, 2579, 2591, 2609, 2647, 2657, 2711, 2741, 2789, 2801, 2819, 2833, 2969, 3011, 3079, 3109, 3119, 3163, 3181, 3187, 3203, 3217, 3251, 3257, 3299, 3343, 3371, 3433, 3457, 3467, 3491, 3607, 3613, 3659, 3697, 3719, 3761, 3793, 3847, 3851, 3877, 3907, 4001, 4091, 4153, 4201, 4259, 4271, 4283, 4327, 4421, 4507, 4513, 4621, 4649, 4729, 4751, 4787, 4813, 4903, 4999, 5167, 5189, 5227, 5323, 5347, 5381, 5441, 5477, 5647, 5683, 5689, 5737, 5779, 5801, 5857, 5923, 6163, 6211, 6217, 6247, 6299, 6311, 6337, 6547, 6563, 6569, 6577, 6659, 6673, 6689, 6701, 6733, 6761, 6791, 6857, 6947, 7039, 7057, 7103, 7151, 7177, 7207, 7211, 7243, 7297, 7307, 7321, 7331, 7393, 7681, 7687, 7699, 7717, 7753, 7817, 7873, 7919, 7927, 7933, 8111, 8167, 8209, 8219, 8231, 8263, 8269, 8287, 8291, 8311, 8387, 8429, 8461, 8521, 8563, 8627, 8641, 8677, 8689, 8819, 8837, 8861, 8963, 8969, 8999, 9011, 9059, 9157, 9277, 9319, 9337, 9371, 9419, 9511, 9547, 9601, 9613, 9619, 9733, 9767, 9781, 9803, 9811, 9829, 9857, 9923, 9929, 10177, 10271, 10289, 10301, 10313, 10331, 10357, 10391, 10453, 10457, 10499, 10529, 10597, 10781, 10949, 11027, 11057, 11273, 11317.

Some larger examples :