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self n.  and  unprimeable n.

First numbers that belong to both sets:

512, 514, 536, 626, 894, 1076, 1144, 1335, 1346, 1412, 1414, 1502, 1682, 1715, 1794, 1895, 2044, 2325, 2402, 2492, 2514, 2516, 2560, 2582, 2942, 2986, 3056, 3146, 3236, 3280, 3482, 3504, 3662, 3684, 3752, 3785, 3818, 3954, 3976, 3998, 4035, 4068, 4180, 4314, 4316, 4382, 4415, 4472, 4685, 4718, 4742, 4764, 4775, 4854, 4898, 4920, 4922, 5126, 5214, 5216, 5315, 5372, 5462, 5495, 5618, 5675, 5754, 5765, 5910, 5945, 5978, 6182, 6406, 6430, 6518, 6720, 6722, 6744, 6755, 6810, 6922, 6924, 6935, 7082, 7115, 7262, 7374, 7385, 7420, 7442, 7464, 7655, 7734, 7778, 7800, 7835, 7890, 7980, 8028, 8072, 8184, 8252, 8342, 8408, 8454, 8476, 8498, 8555, 8610, 8634, 8656, 8722, 8724, 8790, 8858, 8902, 9084, 9218, 9264, 9308, 9354, 9365, 9444, 9455, 9488, 9578, 9758, 9848, 9892, 9914, 9982, 10054, 10122, 10234, 10412, 10414, 10548, 10570, 10805, 10816, 10818, 11200, 11224, 11336, 11402, 11538, 11560, 11604, 11762, 11795, 11852, 11874, 11918, 12056, 12124, 12135, 12315, 12460, 12594, 12662, 12774, 12818, 12864, 12875, 12932, 12998, 13024, 13112, 13114, 13136, 13202, 13270, 13404, 13505, 13540, 13584, 13606, 13652, 13742, 13775, 13865, 13898, 13944, 13955, 13988, 14115, 14126, 14214, 14216, 14238, 14260, 14315, 14350, 14372, 14394, 14495, 14574, 14585, 14618, 14642, 14675, 14708, 14910, 14978, 15000, 15026, 15048, 15114, 15116, 15204, 15485, 15575, 15632, 15654, 15698, 15755, 15834, 15845, 15946, 15968, 16012, 16150, 16172, 16205, 16284, 16295, 16352, 16374, 16396, 16464, 16508, 16532, 16598, 16620, 16622, 16688, 16710, 16734, 16778, 16800, 16868, 16890, 16912, 16958, 17002, 17140, 17274, 17285, 17364, 17454, 17520, 17522, 17544, 17610, 17634, 17645, 17678, 17812, 17948, 17992, 18106, 18152, 18174, 18242, 18275, 18332, 18578, 18600, 18622, 18624, 18646, 18725, 18824, 18826, 18848, 18870, 18925, 18938, 18960, 18982.

Some larger examples :