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emirpimes  and  unprimeable n.

First numbers that belong to both sets:

326, 514, 538, 622, 1135, 1145, 1346, 1354, 1415, 1418, 1466, 1502, 1642, 1714, 1765, 1766, 1795, 1894, 2042, 2402, 2495, 3098, 3142, 3155, 3505, 3665, 3754, 3785, 3814, 3898, 3958, 4145, 4162, 4166, 4195, 4198, 4385, 4535, 4538, 4555, 4574, 4714, 4742, 4765, 5062, 5314, 5318, 5366, 5374, 5378, 5422, 5426, 5455, 5458, 5465, 5498, 5545, 5606, 5615, 5674, 5914, 5942, 6406, 6418, 7082, 7094, 7114, 7135, 7165, 7166, 7262, 7265, 7274, 7318, 7402, 7445, 7655, 7765, 7778, 7834, 7978, 8135, 8158, 8182, 8185, 8306, 8345, 8902, 8914, 8986, 9034, 9038, 9355, 9382, 9442, 9458, 9502, 9578, 9754, 9755, 9895, 9985, 9995, 10085, 10378, 10405, 10546, 10805, 10874, 10966, 11015, 11035, 11302, 11306, 11335, 11378, 11566, 11722, 11854, 11995, 12085, 12086, 12182, 12335, 12365, 13058, 13138, 13274, 13346, 13378, 13582, 13742, 13745, 13814, 13942, 13945, 13954, 13982, 13985, 14138, 14165, 14185, 14218, 14318, 14374, 14458, 14585, 14642, 14702, 14902, 14918, 14974, 14995, 14998, 15118, 15154, 15205, 15482, 15506, 15578, 15658, 15706, 15838, 15898, 16018, 16022, 16045, 16178, 16295, 16322, 16462, 16466, 16535, 16594, 16715, 16735, 16774, 16795, 16805, 16855, 16858, 16865, 16955, 17065, 17218, 17245, 17282, 17305, 17426, 17614, 17635, 17638, 17645, 17965, 17998, 18002, 18022, 18035, 18155, 18206, 18274, 18385, 18562, 18566, 18622, 18646, 18686, 18842, 18965, 18982, 18994, 19094, 19102, 19105, 19174, 19226, 19298, 19354, 19358, 19742, 20035, 20095, 20455, 20465, 20518, 20674, 20765, 20795, 20798, 22045, 22205, 22234, 22238, 22478, 22595, 22846, 22955, 22982, 24298, 24305, 24454, 24602, 24646, 24754, 24835, 24994, 26074, 26126, 26365, 26366, 26545, 26582, 26674, 26914, 26935, 26938, 26974, 28235, 28562, 30146, 30235, 30335, 30455, 30542, 30605, 30746, 30922, 30994, 30995, 31105, 31118, 31166, 31282, 31285, 31294, 31342, 31345, 31366, 31435, 31522.

Some larger examples :