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Smith n.  and  unprimeable n.

First numbers that belong to both sets:

535, 895, 1642, 1678, 1795, 1858, 1894, 1962, 1966, 2182, 2326, 2362, 2366, 2484, 2515, 2944, 3174, 3246, 3505, 3564, 4162, 4185, 4198, 4306, 4414, 4472, 4765, 4855, 5062, 5242, 5248, 5422, 5458, 5602, 5674, 5915, 5946, 5998, 6188, 6502, 6816, 6934, 7136, 7402, 7465, 7762, 7764, 7834, 7978, 8154, 8158, 8185, 8790, 8792, 8874, 8914, 9036, 9355, 9382, 9386, 9598, 9708, 9778, 9840, 9895, 9985, 10086, 10296, 10806, 10966, 11790, 12055, 12318, 12442, 12622, 13506, 13812, 13974, 13984, 14046, 14168, 14458, 14494, 14672, 14998, 15115, 15205, 15704, 15835, 15848, 15860, 15894, 15898, 15984, 16015, 16285, 16294, 16536, 16582, 16592, 16688, 16735, 16770, 16866, 16890, 17086, 17268, 17424, 17455, 17635, 17646, 17698, 17754, 17840, 17940, 18022, 18108, 18274, 18278, 18474, 18562, 18765, 18846, 18872, 18920, 18922, 18985, 18994, 19292, 19360, 19498, 19615, 19644, 19678, 19952, 20578, 20974, 21078, 21478, 21694, 21955, 22234, 22522, 22558, 22585, 22688, 22884, 23242, 23484, 23658, 23694, 23736, 23790, 23962, 24142, 24214, 24306, 24585, 24588, 24754, 24776, 25006, 25064, 25105, 25195, 25294, 25298, 25614, 25618, 25834, 25928, 26365, 26545, 26676, 26760, 26768, 26914, 27085, 27156, 27355, 27382, 27418, 27468, 27562, 27598, 27666, 28174, 28236, 28255, 28336, 28952, 28980, 29182, 29515, 29540, 29542, 29695, 29706, 29772, 29794, 29826, 29890, 29902, 29938, 29960, 30288, 30658, 30906, 31598, 32226, 32278, 32454, 32458, 32552, 32724, 32755, 32854, 32896, 33384, 33680, 34042, 34395, 34555, 34575, 34776, 34832, 34834, 34956, 34978, 35005, 35478, 35635, 35680, 35696, 35784, 35842, 36238, 36335, 36535, 37165, 37476, 37678, 37705, 37820, 37822, 38002, 38074, 38362, 38385, 38388, 38402, 38490, 38515, 38578, 38758, 38965, 39030, 39260, 39426, 39478, 39536, 39570, 39595, 39642, 39685, 39780, 39946, 40398, 40672, 40796, 40954, 41098, 41278, 41376, 41436, 41678, 41746, 42034, 42214, 42272.

Some larger examples :