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emirpimes  and  lucky n.

First numbers that belong to both sets:

15, 49, 51, 93, 115, 129, 159, 169, 205, 289, 319, 321, 327, 339, 415, 511, 553, 559, 685, 723, 781, 933, 961, 1011, 1041, 1057, 1101, 1219, 1357, 1387, 1401, 1417, 1497, 1563, 1641, 1731, 1765, 1797, 1893, 1915, 1923, 1983, 2059, 2257, 2461, 2479, 2491, 2815, 2845, 3007, 3091, 3097, 3099, 3153, 3199, 3261, 3403, 3453, 3481, 3579, 3603, 3669, 3687, 3721, 3891, 3981, 4195, 4321, 4399, 4573, 4963, 5041, 5053, 5191, 5371, 5455, 5515, 5587, 5617, 5671, 5803, 5833, 5893, 5905, 5911, 5971, 5977, 6031, 6049, 6463, 6631, 6667, 7003, 7081, 7087, 7135, 7167, 7171, 7183, 7195, 7233, 7249, 7279, 7311, 7341, 7377, 7401, 7419, 7501, 7531, 7593, 7629, 7711, 7737, 7779, 7795, 7837, 7855, 7899, 7909, 7971, 8131, 8347, 8773, 9033, 9121, 9235, 9267, 9481, 9487, 9501, 9535, 9543, 9663, 9691, 9727, 9753, 9813, 9895, 9979, 9985, 9987, 9997, 10003, 10117, 10195, 10261, 10279, 10363, 10411, 10417, 10671, 10747, 10843, 10873, 10911, 11091, 11157, 11181, 11341, 11371, 11389, 11479, 11539, 11581, 11599, 11629, 11641, 11659, 11667, 11707, 11769, 11797, 11995, 12063, 12133, 12223, 12237, 12399, 12631, 12679, 12709, 12759, 12813, 12877, 12937, 12991, 13011, 13021, 13117, 13141, 13273, 13387, 13657, 13897, 13929, 13947, 14017, 14059, 14073, 14179, 14185, 14353, 14367, 14439, 14493, 14881, 14977, 14997, 15049, 15103, 15109, 15205, 15247, 15261, 15397, 15445, 15487, 15673, 15693, 15783, 15793, 15843, 15927, 15955, 16003, 16009, 16045, 16153, 16197, 16213, 16237, 16255, 16279, 16309, 16387, 16413, 16507, 16591, 16615, 16621, 16639, 16795, 16867, 16953, 16957, 16969, 16971, 17035, 17083, 17221, 17229, 17287, 17305, 17463, 17517, 17527, 17769, 17781, 17893, 17943, 17965, 18001, 18085, 18187, 18589, 18619, 18853, 18937, 18967, 18969, 19015, 19153, 19263, 19405, 19579, 19627, 19693, 19711, 19731.

Some larger examples :