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emirp  and  good prime

First numbers that belong to both sets:

17, 37, 71, 97, 149, 179, 311, 347, 733, 739, 937, 967, 1009, 1031, 1151, 1213, 1399, 1597, 1847, 1867, 3163, 3251, 3299, 3433, 3511, 3527, 3821, 7457, 7523, 9103, 9127, 9133, 9613, 10007, 10061, 10067, 10091, 10853, 11057, 11657, 11677, 11699, 11777, 11897, 12227, 12373, 14293, 14387, 14519, 14713, 15013, 15053, 15227, 16547, 16829, 16879, 16979, 17383, 17827, 17903, 17909, 18899, 18911, 19001, 19421, 19913, 30011, 30059, 30491, 30757, 31121, 31139, 31957, 33287, 33329, 34123, 35729, 35801, 36467, 36523, 38113, 38543, 38557, 38651, 70001, 70913, 73277, 73291, 73327, 73517, 73523, 73939, 74131, 74143, 75167, 76463, 77237, 77471, 79103, 79147, 79531, 79549, 79757, 79769, 79811, 91121, 92143, 92219, 92297, 92311, 92333, 92639, 93871, 93887, 94291, 94397, 97367, 98207, 98317, 98407, 98711, 98801, 98887, 100267, 100357, 101267, 103289, 103391, 103511, 103801, 103963, 104677, 106087, 106103, 106187, 106261, 107687, 107827, 108707, 108739, 108863, 108881, 111427, 111467, 112901, 113011, 114571, 115769, 119489, 119611, 120503, 120539, 120641, 120661, 127207, 127447, 127481, 127637, 128111, 128321, 131437, 132523, 134033, 135389, 136333, 139291, 143239, 143461, 145349, 145391, 148061, 148151, 148361, 148627, 148663, 149053, 150767, 151153, 156619, 156671, 157007, 159389, 159617, 159623, 159671, 160619, 162389, 166147, 166541, 166597, 166601, 168433, 169003, 169217, 169483, 169633, 169649, 175211, 175891, 176191, 177787, 178223, 178393, 178469, 181183, 181199, 181693, 184487, 184607, 184823, 184993, 185531, 189139, 189149, 189307, 189337, 190573, 190577, 195023, 195043, 195047, 196499, 197059, 197203, 197233, 300187, 300481, 302399, 302551, 302573, 302747, 303257, 303283, 311533, 311537, 311951, 311957, 312023, 315247, 316133, 316567, 316621, 316633, 318103, 323333, 324053, 324067, 324089, 324391, 327247, 327401, 333253, 334319, 339991, 340369, 340541, 340573, 340577, 340787, 344167, 345413, 345451, 345571, 345643, 346079, 349369, 350423, 350711, 350941, 361211, 361313, 361763, 362897, 363269, 369791, 370373, 370411, 371027, 371057, 371069.

Some larger examples :