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strong prime  and  super-d n.

First numbers that belong to both sets:

107, 127, 269, 281, 331, 419, 431, 569, 631, 719, 739, 769, 881, 1019, 1031, 1049, 1061, 1181, 1319, 1471, 1481, 1487, 1619, 1847, 1901, 1931, 2081, 2281, 2381, 2473, 2531, 2591, 2819, 2969, 3011, 3019, 3119, 3163, 3181, 3319, 3329, 3343, 3359, 3371, 3389, 3581, 3631, 3719, 3851, 3877, 4019, 4481, 4649, 4931, 5231, 5381, 5431, 5471, 5501, 5519, 5569, 5623, 5981, 6131, 6269, 6469, 6569, 6761, 6791, 6869, 7069, 7151, 7229, 7243, 7331, 7559, 7669, 7681, 7817, 7919, 8081, 8219, 8231, 8269, 8419, 8623, 8731, 8819, 8831, 8969, 9007, 9181, 9281, 9319, 9419, 9431, 9547, 9619, 9719, 9781, 10267, 10301, 10331, 10357, 10499, 10529, 10559, 10589, 10597, 10627, 10651, 10663, 10687, 10709, 10723, 10729, 10781, 10831, 10889, 11069, 11317, 11369, 11519, 11549, 11831, 11969, 11981, 12373, 12569, 12689, 12697, 12781, 12889, 13669, 13781, 13877, 13931, 14081, 14281, 14369, 14419, 14431, 14519, 14533, 14731, 14821, 15131, 15269, 15581, 15619, 15731, 15919, 16319, 16519, 16631, 16741, 17203, 17231, 17569, 17681, 17881, 18059, 18119, 18131, 18169, 18181, 18481, 18617, 19001, 19009, 19031, 19069, 19121, 19181, 19231, 19469, 19531, 19681, 19813, 20219, 20231, 20389, 20431, 20549, 20681, 20981, 21269, 21377, 21481, 21587, 21859, 22381, 22469, 22481, 22531, 22613, 22619, 22669, 22769, 22937, 23011, 23081, 23131, 23269, 23369, 23531, 23581, 23623, 23669, 23687, 23719, 23831, 23869, 24019, 24107, 24169, 24419, 24469, 24611, 24733, 24749, 24763, 24781, 24793, 25031, 25169, 25219, 25469, 25601, 25931, 25969, 26099, 26431, 26479, 26669, 26681, 26947, 26981, 27031, 27281, 27407, 27581, 28019, 28081, 28181, 28619, 29191, 29581, 29669, 29819, 30181, 30269, 30307, 30319, 30631, 30869, 30931, 31181, 31219, 31231, 31319, 31469, 31531, 31769, 32189, 32369, 32467, 32531, 32569, 32831, 32869, 32969, 33179, 33191, 33199, 33287, 33301, 33311, 33329, 33343.

Some larger examples :