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arithmetic n.  and  emirpimes

First numbers that belong to both sets:

15, 39, 49, 51, 62, 85, 93, 94, 115, 123, 129, 143, 155, 158, 159, 169, 177, 183, 185, 187, 203, 205, 221, 265, 302, 319, 321, 326, 327, 329, 335, 339, 341, 355, 381, 398, 413, 415, 437, 493, 497, 502, 511, 533, 551, 553, 559, 581, 589, 622, 623, 629, 667, 685, 718, 723, 734, 766, 771, 781, 817, 835, 851, 871, 893, 899, 913, 921, 923, 926, 933, 951, 955, 961, 982, 985, 998, 1006, 1011, 1027, 1041, 1043, 1046, 1047, 1057, 1059, 1067, 1079, 1101, 1115, 1119, 1121, 1135, 1137, 1141, 1145, 1149, 1165, 1169, 1174, 1177, 1195, 1211, 1214, 1219, 1238, 1243, 1247, 1253, 1273, 1286, 1293, 1299, 1313, 1315, 1317, 1318, 1343, 1347, 1357, 1366, 1371, 1379, 1382, 1383, 1387, 1401, 1405, 1411, 1415, 1417, 1437, 1438, 1454, 1461, 1469, 1497, 1502, 1507, 1513, 1527, 1561, 1563, 1569, 1577, 1623, 1641, 1651, 1655, 1671, 1679, 1687, 1691, 1703, 1707, 1717, 1727, 1731, 1735, 1757, 1761, 1765, 1766, 1769, 1774, 1779, 1795, 1797, 1807, 1814, 1817, 1843, 1849, 1891, 1893, 1894, 1897, 1903, 1915, 1923, 1927, 1937, 1942, 1961, 1969, 1981, 1983, 1985, 2021, 2041, 2047, 2051, 2059, 2062, 2077, 2206, 2219, 2231, 2245, 2257, 2263, 2279, 2413, 2429, 2435, 2443, 2446, 2449, 2461, 2462, 2479, 2491, 2495, 2603, 2605, 2614, 2627, 2654, 2669, 2807, 2815, 2831, 2839, 2845, 2855, 2878, 2881, 3007, 3013, 3043, 3046, 3047, 3053, 3062, 3063, 3065, 3071, 3085, 3091, 3093, 3097, 3099, 3103, 3117, 3131, 3134, 3139, 3142, 3151, 3153, 3155, 3166, 3173, 3189, 3197, 3199, 3207, 3215, 3227, 3247, 3261, 3291, 3305, 3309, 3317, 3326, 3327, 3334, 3365, 3385, 3401, 3403, 3415, 3419, 3421, 3431, 3437, 3446, 3453, 3455.

Some larger examples :