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congruent n.  and  emirpimes

First numbers that belong to both sets:

15, 39, 62, 85, 93, 94, 143, 158, 159, 183, 205, 221, 226, 265, 302, 319, 326, 327, 335, 341, 381, 398, 413, 415, 437, 493, 502, 511, 514, 533, 551, 559, 581, 589, 622, 623, 629, 685, 718, 723, 734, 766, 781, 871, 893, 926, 933, 951, 982, 985, 998, 1006, 1046, 1047, 1057, 1079, 1101, 1119, 1135, 1141, 1145, 1149, 1154, 1165, 1169, 1174, 1195, 1214, 1238, 1247, 1253, 1286, 1293, 1317, 1318, 1343, 1346, 1357, 1366, 1379, 1382, 1383, 1387, 1405, 1411, 1415, 1437, 1438, 1454, 1461, 1469, 1502, 1513, 1527, 1561, 1623, 1651, 1655, 1671, 1679, 1687, 1703, 1717, 1727, 1731, 1735, 1757, 1765, 1766, 1774, 1797, 1807, 1814, 1893, 1894, 1903, 1927, 1942, 1981, 1983, 2021, 2047, 2059, 2062, 2077, 2206, 2231, 2245, 2257, 2263, 2279, 2413, 2429, 2446, 2461, 2462, 2479, 2495, 2605, 2614, 2654, 2669, 2807, 2815, 2818, 2831, 2839, 2845, 2855, 2878, 3007, 3013, 3046, 3047, 3053, 3062, 3063, 3071, 3085, 3093, 3099, 3103, 3117, 3134, 3142, 3151, 3166, 3173, 3189, 3197, 3199, 3207, 3215, 3247, 3261, 3309, 3317, 3326, 3327, 3334, 3365, 3415, 3421, 3431, 3437, 3446, 3453, 3455, 3503, 3518, 3543, 3554, 3589, 3599, 3603, 3622, 3629, 3639, 3646, 3647, 3653, 3669, 3679, 3687, 3693, 3694, 3695, 3713, 3743, 3778, 3814, 3831, 3839, 3869, 3893, 3899, 3903, 3949, 3957, 3958, 3959, 3981, 3983, 3985, 4109, 4117, 4121, 4135, 4151, 4166, 4174, 4181, 4183, 4198, 4309, 4319, 4333, 4399, 4511, 4535, 4541, 4573, 4574, 4711, 4727, 4735, 4742, 4765, 4781, 4981, 5006, 5053, 5062, 5078, 5086, 5095, 5111, 5141, 5143, 5165, 5173, 5182, 5191, 5311, 5314, 5317, 5318, 5327, 5342, 5359, 5366, 5374, 5398, 5414, 5422, 5438, 5447, 5455, 5465, 5509.

Some larger examples :