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interprime n.  and  Smith n.

First numbers that belong to both sets:

4, 274, 483, 636, 645, 825, 861, 915, 1449, 1581, 1795, 1872, 1962, 2475, 2688, 2745, 2751, 2970, 3168, 3258, 3345, 3366, 3390, 3505, 3615, 3694, 3852, 3930, 4054, 4189, 4472, 4594, 4788, 4954, 5854, 5874, 5946, 6084, 6096, 6252, 6603, 6684, 6702, 7402, 7503, 7695, 7978, 8014, 8154, 8185, 8253, 8421, 8568, 8628, 9184, 9193, 9330, 9346, 9684, 9708, 10689, 10736, 11388, 11583, 11679, 11984, 12573, 12656, 12795, 12847, 13454, 13506, 13905, 14085, 14756, 14998, 15126, 15884, 16735, 16744, 16902, 16940, 17664, 17838, 17916, 18069, 18108, 18132, 18278, 18454, 18459, 18675, 18765, 19212, 19376, 19428, 19590, 19606, 19761, 19943, 20578, 21078, 21273, 21615, 21667, 22117, 22368, 22386, 22558, 22983, 23163, 25177, 25844, 26295, 26637, 26682, 26734, 26768, 26892, 27247, 27382, 27418, 27468, 27546, 27639, 27792, 27950, 28182, 28662, 28840, 28905, 29529, 29760, 29826, 30138, 30390, 30397, 30523, 31693, 31746, 32118, 32197, 32418, 32786, 32793, 33384, 33633, 33880, 35239, 35358, 35397, 35784, 35806, 36090, 36296, 36535, 36555, 36680, 37165, 37374, 37822, 37960, 38238, 38385, 38758, 38864, 38965, 39084, 39307, 39456, 40234, 40477, 40587, 40594, 41624, 42495, 42780, 43287, 43737, 44028, 44619, 45069, 45186, 46056, 46318, 46563, 46590, 46809, 47029, 47155, 47244, 47646, 47925, 47943, 48793, 48858, 49131, 49351, 49423, 49941, 50926, 51545, 51846, 51945, 52278, 52366, 52514, 52618, 52960, 53560, 53626, 54006, 54234, 54553, 54582, 54639, 54814, 54992, 55606, 55977, 56047, 56096, 56208, 57255, 57339, 57477, 57651, 58374, 58414, 58446, 58590, 59080, 59175, 59307, 59485, 60090, 60642, 60888, 61429, 61490, 61984, 62216, 62504, 62694, 62985, 64086, 64494, 64572, 64788, 65007, 65169, 65376, 65841, 65859, 66440, 66636, 66717, 66870, 66990, 67067, 67281, 67704, 67728, 68490, 68802, 68955, 69135, 69381, 69750, 70029, 70089, 70362, 70929, 70974, 71581, 71864, 72075, 72274, 72695, 72841.

Some larger examples :