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emirpimes  and  pernicious n.

First numbers that belong to both sets:

26, 49, 62, 93, 94, 115, 122, 129, 143, 155, 158, 185, 203, 205, 265, 289, 302, 314, 319, 321, 327, 339, 341, 355, 381, 398, 415, 493, 502, 514, 551, 589, 623, 734, 781, 794, 817, 835, 871, 899, 913, 923, 926, 961, 982, 985, 998, 1027, 1041, 1047, 1057, 1067, 1101, 1119, 1135, 1137, 1149, 1154, 1165, 1174, 1177, 1202, 1211, 1214, 1219, 1234, 1243, 1273, 1293, 1299, 1306, 1315, 1317, 1318, 1322, 1347, 1354, 1371, 1383, 1387, 1401, 1402, 1411, 1417, 1418, 1437, 1438, 1454, 1461, 1466, 1497, 1507, 1513, 1514, 1538, 1561, 1577, 1623, 1651, 1658, 1679, 1687, 1691, 1703, 1707, 1717, 1735, 1754, 1765, 1766, 1769, 1795, 1797, 1807, 1843, 1849, 1882, 1891, 1893, 1894, 1897, 1927, 1942, 1961, 1969, 2018, 2047, 2051, 2066, 2077, 2231, 2245, 2257, 2258, 2263, 2279, 2402, 2413, 2426, 2435, 2449, 2461, 2462, 2602, 2627, 2642, 2654, 2669, 2831, 2839, 2845, 2855, 2881, 3013, 3071, 3085, 3091, 3093, 3097, 3098, 3103, 3131, 3134, 3139, 3142, 3151, 3153, 3166, 3189, 3215, 3227, 3305, 3334, 3338, 3385, 3403, 3418, 3442, 3481, 3505, 3554, 3589, 3599, 3629, 3635, 3667, 3669, 3713, 3737, 3754, 3785, 3809, 3839, 3866, 3921, 3985, 3986, 4135, 4162, 4171, 4174, 4181, 4195, 4198, 4321, 4322, 4333, 4387, 4399, 4531, 4537, 4538, 4555, 4579, 4594, 4711, 4742, 4754, 4765, 4781, 4907, 4954, 4963, 5006, 5033, 5041, 5062, 5131, 5141, 5155, 5182, 5314, 5354, 5386, 5422, 5447, 5465, 5482, 5515, 5539, 5545, 5554, 5585, 5671, 5677, 5686, 5833, 5834, 5899, 5914, 5926, 6022, 6049, 6242, 6295, 6403, 6406, 6418, 6439, 6443, 6458, 6499, 6602, 6671, 6683, 6686, 6805, 6821, 6865, 6866, 7058, 7073, 7135, 7165, 7166, 7171, 7183, 7186, 7195, 7201.

Some larger examples :