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good prime  and  super-d n.

First numbers that belong to both sets:

127, 269, 331, 419, 431, 569, 739, 1031, 1847, 2531, 3163, 4481, 4931, 5381, 5623, 6761, 8081, 8219, 8623, 9319, 10589, 10597, 10831, 12373, 12889, 13669, 14369, 14519, 14533, 15269, 17881, 19001, 20681, 20981, 21377, 21481, 22531, 22613, 22619, 23531, 24763, 26669, 26681, 27407, 30631, 32969, 33287, 33311, 33329, 35729, 35747, 35831, 38669, 40471, 40739, 40759, 40819, 41131, 41879, 41947, 45943, 47119, 47269, 48731, 49103, 51109, 51131, 51197, 51419, 54269, 54319, 55619, 55787, 55793, 56369, 56377, 56431, 61331, 61463, 61469, 62459, 64997, 65519, 66919, 70099, 71143, 73547, 74131, 74707, 77471, 79031, 79531, 79757, 79769, 80471, 80669, 84179, 86069, 89519, 91753, 92219, 98207, 98369, 101081, 103549, 104471, 105227, 106087, 106103, 106163, 106181, 106187, 106207, 106261, 106273, 107581, 108877, 108881, 110419, 110431, 113011, 115547, 115769, 116903, 119489, 120539, 127031, 127481, 128287, 131431, 132619, 136319, 143239, 145349, 145381, 145391, 145417, 148331, 150869, 150881, 156589, 156619, 160619, 175601, 175631, 176327, 178469, 178481, 181889, 184949, 185519, 185531, 189139, 194681, 195731, 196499, 201731, 201781, 205019, 205031, 206803, 206909, 207169, 207433, 216569, 216719, 216731, 218069, 218081, 227081, 228181, 228281, 228419, 234131, 234181, 236377, 236681, 238079, 238141, 243431, 244351, 246119, 246469, 246599, 250619, 250681, 253531, 253607, 254869, 257219, 262109, 264731, 266663, 266671, 266677, 267131, 267373, 273881, 275881, 275897, 275911, 275917, 278489, 289019, 295699, 295819, 295831, 298579, 299261, 299281, 299357, 299881, 300187, 300481, 300569, 300581, 302831, 302969, 313471, 316031, 317263, 324419, 332987, 333253, 333269, 334289, 334319, 334331, 334379, 334987, 335999, 336029, 336101, 336491, 336499, 336521, 336527, 339583, 339631, 340369, 340381, 340519, 340577, 340757, 340777, 340787, 349369, 360769, 360779, 362863, 363269, 371027, 371069, 371131, 371831, 374669, 374681, 382331, 383483, 383519, 388777, 388859, 389437, 404969, 407119, 413681, 416989, 417169, 417719, 426631, 426731, 429083, 429119, 429181, 430511, 430649, 430739, 448519, 455149, 462373.

Some larger examples :