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emirp  and  pernicious n.

First numbers that belong to both sets:

13, 17, 31, 37, 73, 79, 97, 107, 157, 167, 179, 199, 701, 709, 733, 743, 761, 769, 941, 953, 967, 971, 1009, 1033, 1069, 1109, 1153, 1193, 1201, 1213, 1231, 1249, 1259, 1301, 1321, 1453, 1583, 1597, 1657, 1669, 1741, 1753, 1831, 1867, 1933, 3011, 3083, 3109, 3121, 3163, 3169, 3203, 3251, 3257, 3271, 3299, 3301, 3343, 3371, 3373, 3433, 3463, 3467, 3469, 3583, 3613, 3697, 3719, 3733, 3851, 3853, 3889, 7043, 7057, 7177, 7207, 7219, 7253, 7297, 7321, 7459, 7561, 7681, 7687, 7699, 7717, 7817, 7841, 7927, 9011, 9013, 9161, 9227, 9241, 9257, 9349, 9421, 9547, 9601, 9613, 9781, 9803, 9833, 9857, 9923, 10009, 10177, 10247, 10253, 10321, 10333, 10343, 10391, 10453, 10457, 10499, 10781, 10853, 10891, 11057, 11329, 11353, 11489, 11587, 11593, 11657, 11777, 11783, 11789, 11903, 11909, 11969, 12253, 12269, 12289, 12301, 12323, 12491, 12547, 12553, 12577, 12619, 12697, 12713, 12799, 12809, 12829, 13009, 13441, 13477, 13513, 13759, 13873, 14071, 14143, 14323, 14387, 14449, 14591, 14593, 14629, 14633, 14831, 14843, 14897, 14929, 15101, 15227, 15263, 15349, 15493, 15497, 15649, 15679, 15791, 15803, 15937, 16001, 16103, 16127, 16249, 16427, 16547, 16567, 16573, 16603, 16651, 16699, 16747, 16937, 16943, 17011, 17033, 17041, 17047, 17203, 17209, 17443, 17467, 17477, 17579, 17669, 17681, 17747, 17749, 17827, 17923, 17959, 18089, 18307, 18427, 18439, 18539, 18593, 18637, 18691, 18731, 18773, 18787, 18913, 19001, 19219, 19237, 19249, 19333, 19423, 19471, 19489, 19531, 19541, 19681, 19793, 30139, 30197, 30271, 30319, 30367, 30557, 30643, 30649, 30757, 30851, 30853, 30881, 30911, 30971, 31183, 31327, 31481, 31543, 31643, 31721, 31741, 31873, 31963, 31981, 32143, 32173, 32203, 32213, 32233, 32257, 32303, 32377, 32411, 32441, 32467, 32479, 32497, 32563, 32647, 32687, 32713, 32749, 32783, 32869, 32887, 32933, 32983, 32999.

Some larger examples :