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emirp  and  odious n.

First numbers that belong to both sets:

13, 31, 37, 73, 79, 97, 107, 157, 167, 179, 199, 701, 709, 733, 743, 761, 769, 941, 953, 967, 971, 991, 1009, 1021, 1033, 1069, 1109, 1153, 1193, 1201, 1213, 1231, 1249, 1259, 1279, 1301, 1321, 1453, 1471, 1583, 1597, 1657, 1669, 1741, 1753, 1789, 1831, 1867, 1933, 1979, 3011, 3023, 3083, 3109, 3121, 3163, 3169, 3203, 3251, 3257, 3271, 3299, 3301, 3319, 3343, 3371, 3373, 3391, 3433, 3463, 3467, 3469, 3511, 3571, 3583, 3613, 3697, 3719, 3733, 3767, 3803, 3821, 3851, 3853, 3889, 7027, 7043, 7057, 7177, 7207, 7219, 7253, 7297, 7321, 7459, 7561, 7603, 7681, 7687, 7699, 7717, 7817, 7841, 7879, 7927, 7951, 7963, 9011, 9013, 9161, 9209, 9227, 9241, 9257, 9349, 9421, 9439, 9467, 9547, 9601, 9613, 9661, 9679, 9721, 9781, 9791, 9803, 9833, 9857, 9923, 10009, 10039, 10091, 10151, 10177, 10247, 10253, 10321, 10333, 10343, 10391, 10453, 10457, 10487, 10499, 10711, 10739, 10781, 10853, 10891, 10939, 10987, 11057, 11159, 11329, 11353, 11423, 11447, 11489, 11551, 11579, 11587, 11593, 11657, 11677, 11699, 11701, 11719, 11731, 11777, 11783, 11789, 11897, 11903, 11909, 11927, 11933, 11969, 11981, 12071, 12107, 12109, 12227, 12241, 12253, 12269, 12289, 12301, 12323, 12491, 12547, 12553, 12577, 12619, 12697, 12713, 12763, 12799, 12809, 12829, 12919, 12983, 13009, 13043, 13147, 13159, 13163, 13259, 13267, 13297, 13441, 13477, 13499, 13513, 13711, 13759, 13781, 13873, 13903, 13933, 14029, 14057, 14071, 14107, 14143, 14221, 14323, 14387, 14431, 14447, 14449, 14519, 14551, 14557, 14591, 14593, 14629, 14633, 14713, 14821, 14831, 14843, 14879, 14897, 14929, 14939, 14957, 15053, 15101, 15131, 15149, 15227, 15263, 15299, 15349, 15493, 15497, 15511, 15527, 15541, 15601, 15643, 15649, 15661, 15667, 15679, 15791, 15803, 15937, 15973, 16001, 16007, 16073, 16103, 16127, 16249, 16427, 16547, 16567, 16573.

Some larger examples :