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super-d n.  and  weak prime

First numbers that belong to both sets:

19, 31, 131, 181, 337, 601, 619, 919, 1051, 1063, 1069, 1231, 1381, 1453, 1531, 1669, 1831, 2069, 2131, 2269, 2477, 2719, 2731, 3169, 3323, 3331, 3347, 3361, 3373, 3391, 3469, 3623, 3769, 3881, 3919, 3931, 4219, 4231, 4261, 4451, 4519, 4831, 4919, 4969, 5011, 5081, 5119, 5281, 5419, 5531, 5581, 5669, 5869, 5881, 6011, 6133, 6481, 6581, 6619, 6719, 6781, 6793, 7019, 7079, 7219, 7369, 7481, 7829, 8011, 8069, 8369, 8431, 8581, 8609, 8669, 8681, 8719, 9623, 9631, 9769, 9931, 9949, 10069, 10169, 10181, 10369, 10501, 10513, 10531, 10567, 10601, 10613, 10631, 10639, 10667, 10691, 10711, 10739, 10753, 10861, 10891, 11119, 11131, 11471, 11681, 11719, 12119, 12269, 12281, 12479, 12619, 12703, 12919, 13219, 13331, 13381, 13469, 13619, 13681, 13831, 14489, 14537, 14669, 14831, 14869, 14969, 15031, 15199, 15319, 15331, 15511, 15569, 15739, 15881, 16069, 16231, 16369, 16381, 16481, 16831, 16903, 16931, 16981, 17209, 17419, 17471, 17491, 17497, 17519, 17581, 17627, 17669, 17981, 18257, 18269, 18503, 18719, 18869, 18919, 19013, 19081, 19219, 19319, 19381, 19471, 19489, 19777, 19819, 19919, 20177, 20269, 20369, 20399, 20719, 20753, 21019, 21031, 21169, 21319, 21419, 21569, 21881, 22031, 22307, 22369, 23063, 23297, 23431, 23689, 23819, 23981, 24181, 24251, 24281, 24481, 24631, 24709, 24767, 24799, 24919, 25127, 25247, 25471, 25679, 25717, 25819, 25919, 25981, 26119, 26573, 26731, 26881, 27431, 27481, 27631, 27919, 27943, 28031, 28219, 28319, 28631, 28669, 28753, 29131, 29231, 29347, 29531, 29569, 29611, 29633, 29881, 30119, 30169, 30187, 30347, 30391, 30431, 30469, 30649, 30781, 30881, 31019, 31069, 31081, 31123, 31357, 31481, 31799, 31981, 32069, 32119, 32381, 32537, 32573, 32579, 32719, 33119, 33181, 33203, 33211, 33223, 33247, 33289, 33317, 33331, 33349, 33353, 33359, 33413, 33427, 33461, 33469, 33493, 33503, 33533, 33547, 33569, 33581, 33589, 33601.

Some larger examples :