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interprime n.  and  unprimeable n.

First numbers that belong to both sets:

324, 515, 532, 625, 846, 1078, 1140, 1268, 1344, 1416, 1465, 1505, 1715, 1768, 1795, 1854, 1895, 1922, 1962, 2046, 2075, 2105, 2322, 2364, 2405, 2490, 2512, 2568, 2585, 2826, 2946, 2985, 3055, 3150, 3175, 3240, 3265, 3285, 3480, 3505, 3565, 3665, 3684, 3750, 3786, 3812, 3898, 3978, 3995, 4038, 4065, 4085, 4105, 4146, 4168, 4312, 4382, 4415, 4432, 4472, 4535, 4555, 4575, 4612, 4685, 4712, 4742, 4824, 4846, 4896, 4925, 5045, 5068, 5218, 5316, 5366, 5425, 5460, 5492, 5544, 5676, 5764, 5946, 6185, 6238, 6438, 6506, 6538, 6628, 6645, 6726, 6932, 7115, 7140, 7168, 7268, 7315, 7402, 7425, 7442, 7468, 7614, 7734, 7774, 7805, 7835, 7892, 7978, 8028, 8046, 8075, 8135, 8154, 8185, 8304, 8404, 8454, 8484, 8616, 8635, 8655, 8725, 8855, 8908, 8985, 9035, 9118, 9144, 9215, 9302, 9360, 9384, 9450, 9485, 9504, 9594, 9655, 9708, 9758, 9775, 9845, 9865, 9894, 9915, 9958, 9990, 10050, 10085, 10122, 10202, 10295, 10380, 10545, 10578, 10645, 10746, 10762, 10815, 10875, 10965, 11015, 11125, 11205, 11226, 11305, 11340, 11376, 11405, 11538, 11565, 11645, 11725, 11760, 11795, 11916, 12024, 12060, 12085, 12180, 12295, 12312, 12336, 12360, 12385, 12444, 12465, 12595, 12628, 12665, 12772, 12815, 12835, 12932, 12992, 13056, 13078, 13115, 13202, 13235, 13374, 13405, 13506, 13545, 13584, 13605, 13740, 13772, 13818, 13866, 13892, 13948, 13982, 14042, 14064, 14125, 14166, 14214, 14232, 14266, 14312, 14334, 14358, 14378, 14395, 14455, 14496, 14526, 14646, 14676, 14706, 14805, 14910, 14976, 14998, 15024, 15042, 15114, 15155, 15208, 15504, 15534, 15575, 15592, 15635, 15655, 15705, 15755, 15868, 15895, 15948, 15965, 15982, 16020, 16045, 16162, 16205, 16326, 16355, 16375, 16396, 16465, 16506, 16538, 16588, 16625, 16682, 16716, 16735, 16775, 16895, 16912, 17002, 17065, 17085, 17148, 17175, 17220, 17248, 17274, 17308.

Some larger examples :