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emirpimes  and  interprime n.

First numbers that belong to both sets:

15, 26, 39, 93, 129, 205, 381, 667, 723, 771, 933, 1011, 1234, 1243, 1286, 1299, 1313, 1527, 1563, 1569, 1795, 1817, 1983, 2066, 2627, 3099, 3189, 3197, 3326, 3453, 3459, 3505, 3651, 3665, 3694, 3898, 3921, 3957, 4535, 4555, 4594, 4742, 4771, 4954, 5006, 5366, 5513, 5686, 5833, 6613, 6667, 6866, 7023, 7233, 7341, 7402, 7597, 7646, 7913, 7957, 7978, 8135, 8185, 8314, 8341, 8507, 9097, 9167, 9267, 9346, 9543, 9569, 9727, 9797, 10085, 10217, 10363, 10677, 10717, 10886, 11015, 11103, 11267, 11293, 11314, 11477, 11667, 11829, 11851, 11906, 11947, 12085, 12146, 12233, 12494, 12871, 12891, 13021, 13106, 13353, 13641, 13703, 13917, 13982, 14054, 14631, 14727, 14837, 14954, 14998, 15167, 15261, 15441, 15613, 15681, 16045, 16251, 16613, 16667, 16735, 16753, 16837, 16886, 16953, 16971, 17065, 17197, 17474, 17494, 17503, 17817, 17857, 17965, 18001, 18129, 18159, 18547, 18649, 18707, 18737, 18953, 19011, 19243, 19263, 19419, 19606, 19713, 19797, 20057, 20095, 20527, 20546, 20687, 20765, 20798, 22045, 22238, 22421, 22546, 22874, 22889, 24226, 24602, 24694, 24787, 24883, 24974, 26443, 26507, 26567, 26582, 26594, 26734, 28117, 28157, 28286, 28646, 30021, 30111, 30397, 30813, 30934, 31389, 31693, 32066, 32197, 32254, 32259, 32366, 32374, 32455, 32519, 32583, 33406, 33691, 33717, 34135, 34165, 34477, 34597, 34761, 34813, 34955, 35135, 35151, 35314, 35413, 35499, 35515, 35582, 35957, 36257, 36471, 36535, 36773, 36937, 37131, 37403, 37491, 37514, 37613, 37822, 38293, 38733, 38758, 38797, 38882, 38919, 39297, 39441, 39557, 39613, 39691, 41186, 41369, 41485, 41546, 41774, 41857, 43057, 43361, 43454, 43994, 45134, 45547, 47198, 47626, 49163, 49319, 50399, 50533, 50783, 51335, 53123, 53155, 53626, 53687, 53894, 53945, 54187, 54553, 54793, 54814, 55015, 55054, 55478, 55694, 56047, 56107, 56605, 58414, 59485, 59666, 59821, 60446, 60595, 62441, 62954, 66353, 66479.

Some larger examples :