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good prime  and  pernicious n.

First numbers that belong to both sets:

5, 11, 17, 37, 41, 59, 67, 97, 127, 179, 191, 223, 227, 251, 257, 307, 331, 419, 431, 541, 557, 563, 569, 587, 641, 727, 733, 809, 929, 967, 1009, 1087, 1213, 1367, 1423, 1543, 1597, 1867, 1987, 1993, 2063, 2237, 2267, 2339, 2521, 2531, 2609, 2647, 2657, 2677, 3163, 3251, 3299, 3433, 3457, 3847, 3907, 4001, 4201, 4507, 4621, 4903, 5381, 5647, 6547, 6563, 6659, 6689, 6761, 6947, 8167, 8209, 8219, 8521, 8677, 8689, 8999, 9277, 9319, 9337, 9371, 9397, 9613, 10597, 10853, 11057, 11657, 11777, 12239, 12473, 12487, 12889, 14369, 14387, 14401, 14407, 14533, 15227, 16411, 16417, 16547, 16811, 17291, 17317, 17377, 17827, 19001, 19139, 19207, 20707, 20849, 21139, 21487, 21557, 22531, 22613, 22691, 22697, 23531, 24841, 24907, 24917, 25087, 25111, 25117, 25537, 26669, 26681, 27397, 27611, 27673, 27689, 28403, 28537, 28571, 28597, 29833, 30631, 30637, 30757, 32969, 33287, 33311, 33329, 34123, 35729, 35831, 36433, 36671, 38113, 38593, 38651, 39089, 40423, 40427, 40693, 40697, 40751, 40759, 40813, 40819, 41039, 41131, 41141, 41177, 45943, 46091, 46399, 47051, 47087, 47111, 48311, 48463, 48731, 48757, 48973, 49103, 50821, 50833, 51131, 51193, 51329, 51341, 54251, 55787, 56431, 58889, 58897, 61211, 61283, 61331, 61441, 62459, 62467, 63277, 64567, 65099, 65353, 65537, 66337, 66343, 66457, 66697, 69653, 70001, 70913, 73327, 73939, 73999, 74017, 74131, 74687, 77471, 79087, 79549, 79801, 80447, 80599, 84053, 84121, 86011, 86069, 88807, 91807, 92107, 92143, 92173, 92297, 92353, 92623, 93851, 93887, 97367, 98179, 98317, 98407, 98867, 98887, 98893, 100333, 100357, 101111, 103387, 104459, 106087, 106163, 106187, 106207, 108791, 108863, 110419, 110431, 110477, 110557, 111467, 111487, 113011, 114451, 114467, 114547, 114593, 114599, 119503, 119533, 119611, 120661, 120811, 127207, 127579, 127591, 127597, 128339, 131431, 131437, 131671, 131687, 131701, 132229, 132491, 132607.

Some larger examples :