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Duffinian n.  and  emirpimes

First numbers that belong to both sets:

39, 49, 85, 93, 115, 129, 143, 155, 169, 183, 185, 187, 203, 205, 221, 265, 289, 319, 327, 329, 335, 341, 355, 381, 413, 415, 437, 493, 497, 511, 533, 551, 553, 559, 589, 623, 629, 667, 685, 723, 781, 817, 835, 851, 871, 893, 899, 913, 921, 923, 955, 961, 985, 1011, 1027, 1043, 1047, 1057, 1067, 1079, 1101, 1115, 1119, 1121, 1135, 1137, 1141, 1165, 1177, 1211, 1219, 1243, 1247, 1253, 1273, 1299, 1313, 1315, 1317, 1343, 1357, 1371, 1379, 1387, 1405, 1411, 1415, 1417, 1461, 1469, 1497, 1507, 1513, 1569, 1577, 1623, 1641, 1651, 1655, 1679, 1687, 1691, 1703, 1727, 1731, 1735, 1765, 1769, 1807, 1817, 1843, 1849, 1893, 1897, 1903, 1915, 1927, 1937, 1961, 1969, 1981, 1983, 1985, 2021, 2041, 2047, 2059, 2077, 2219, 2231, 2257, 2263, 2279, 2413, 2429, 2435, 2449, 2461, 2479, 2491, 2603, 2605, 2627, 2669, 2807, 2815, 2831, 2839, 2855, 2881, 3007, 3013, 3043, 3047, 3053, 3063, 3065, 3071, 3085, 3091, 3097, 3099, 3103, 3117, 3131, 3139, 3153, 3155, 3173, 3189, 3197, 3199, 3207, 3215, 3247, 3261, 3305, 3317, 3365, 3385, 3401, 3403, 3415, 3419, 3421, 3431, 3437, 3455, 3459, 3473, 3481, 3503, 3505, 3513, 3563, 3589, 3599, 3603, 3629, 3635, 3639, 3647, 3653, 3665, 3667, 3679, 3693, 3707, 3713, 3715, 3721, 3737, 3743, 3785, 3809, 3817, 3839, 3869, 3891, 3893, 3899, 3949, 3959, 3963, 3979, 3981, 3983, 3985, 4115, 4117, 4121, 4135, 4151, 4171, 4181, 4183, 4187, 4307, 4309, 4319, 4321, 4333, 4369, 4385, 4387, 4399, 4511, 4531, 4535, 4537, 4541, 4553, 4555, 4571, 4573, 4577, 4579, 4711, 4727, 4735, 4765, 4771, 4781, 4907, 4955, 4963, 4981, 5033, 5041, 5053, 5111, 5123, 5131, 5141, 5143, 5155, 5165, 5173, 5177, 5191.

Some larger examples :