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emirpimes  and  happy n.

First numbers that belong to both sets:

49, 94, 129, 203, 226, 302, 319, 326, 329, 622, 623, 899, 913, 921, 923, 998, 1067, 1115, 1121, 1141, 1177, 1211, 1247, 1299, 1366, 1411, 1418, 1527, 1679, 1706, 1717, 1727, 1754, 1769, 1814, 1874, 1882, 1903, 2062, 2206, 2245, 2257, 2258, 2458, 2602, 2603, 2815, 2818, 2845, 2881, 3013, 3062, 3065, 3091, 3097, 3103, 3139, 3153, 3166, 3173, 3317, 3338, 3365, 3513, 3563, 3629, 3635, 3646, 3653, 3667, 3713, 3869, 3986, 4174, 4178, 4181, 4187, 4555, 4571, 4577, 4714, 4781, 5111, 5182, 5363, 5422, 5455, 5458, 5482, 5545, 5554, 5585, 5603, 5606, 5633, 5855, 6022, 6038, 6049, 6065, 6071, 6239, 6463, 6613, 6631, 6893, 7133, 7169, 7171, 7251, 7271, 7421, 7522, 7601, 7619, 7663, 7711, 7754, 7814, 7903, 8141, 8182, 8306, 8333, 8522, 8542, 8545, 8714, 8759, 8909, 9089, 9098, 9167, 9263, 9313, 9326, 9406, 9578, 9617, 9671, 9683, 9761, 9809, 9921, 10003, 10033, 10411, 10447, 10474, 10717, 10874, 10882, 10967, 11015, 11051, 11147, 11179, 11181, 11195, 11215, 11249, 11267, 11314, 11341, 11401, 11413, 11465, 11591, 11654, 11707, 11714, 11741, 11773, 11791, 11843, 11917, 12074, 12077, 12081, 12085, 12202, 12226, 12262, 12283, 12286, 12297, 12399, 12407, 12419, 12526, 12599, 12707, 12761, 12767, 12813, 12877, 13073, 13141, 13142, 13274, 13307, 13343, 13393, 13418, 13582, 13663, 13703, 13742, 13745, 13814, 13929, 14117, 14129, 14131, 14138, 14165, 14167, 14171, 14183, 14213, 14218, 14219, 14237, 14273, 14291, 14311, 14318, 14374, 14486, 14507, 14594, 14617, 14702, 14711, 14837, 14873, 14954, 15011, 15154, 15191, 15286, 15347, 15357, 15415, 15514, 15537, 15682, 15734, 15769, 15802, 15967, 16118, 16145, 16222, 16255, 16271, 16397, 16679, 16697, 16721, 16795, 16858, 16957, 17054, 17141, 17229, 17243, 17261, 17267, 17287, 17354, 17369, 17453, 17543, 17614, 17639, 17726, 17735, 17857, 17858.

Some larger examples :