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emirpimes  and  self n.

First numbers that belong to both sets:

143, 187, 413, 514, 771, 817, 951, 1006, 1043, 1177, 1234, 1313, 1346, 1357, 1379, 1401, 1469, 1502, 1513, 1671, 1717, 1761, 1985, 2066, 2077, 2257, 2279, 2402, 2413, 2426, 3247, 3291, 3326, 3403, 3629, 3651, 3695, 3785, 3831, 3921, 4562, 4573, 4742, 4955, 5317, 5339, 5585, 5686, 5833, 5855, 5899, 5989, 6239, 6283, 6406, 6463, 6821, 6889, 7071, 7082, 7183, 7251, 7262, 7341, 7431, 7655, 7666, 7778, 7846, 8522, 8566, 8735, 8902, 9014, 9242, 9466, 9578, 9611, 9701, 9813, 9903, 9938, 10109, 10447, 10537, 10603, 10671, 10717, 10805, 10873, 10895, 10919, 11099, 11189, 11246, 11314, 11413, 11459, 11582, 11729, 11751, 11773, 11841, 11885, 12067, 12146, 12302, 12359, 12403, 12471, 12605, 12629, 12706, 12785, 13382, 13393, 13439, 13529, 13562, 13595, 13641, 13663, 13742, 13819, 13843, 13922, 14069, 14227, 14339, 14383, 14429, 14451, 14506, 14585, 14631, 14642, 14719, 14765, 14855, 14989, 15011, 15103, 15127, 15261, 15305, 15362, 15406, 15419, 15441, 15553, 15709, 15821, 16251, 16295, 16442, 16486, 16565, 16609, 16721, 16723, 16846, 16923, 16969, 17039, 17083, 17129, 17219, 17421, 17533, 17555, 17645, 17711, 17722, 17735, 17801, 17858, 17869, 17902, 18163, 18185, 18365, 18455, 18499, 18589, 18622, 18646, 18769, 18813, 18949, 18982, 19015, 19153, 19243, 19265, 19298, 19445, 19511, 19579, 19702, 19713, 19814, 19849, 19882, 19939, 20077, 20459, 20527, 20617, 20729, 20795, 20863, 20885, 22327, 22529, 22595, 22663, 22786, 22955, 22966, 24011, 24193, 24283, 24305, 24619, 24643, 24823, 26219, 26443, 26689, 26735, 26926, 28298, 28333, 28445, 28511, 28781, 28838, 28849, 30111, 30146, 30157, 30359, 30605, 30629, 30662, 30673, 30886, 31169, 31439, 31461, 31483, 31529, 31718, 31753, 31821, 31843, 31909, 31933, 32047, 32137, 32293, 32506, 32519, 32743, 32765, 32822, 32866, 33081, 33127, 33171, 33373, 33406, 33643, 33709, 33821, 34049, 34082, 34115, 34139, 34205.

Some larger examples :