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sphenic n.  and  untouchable n.

First numbers that belong to both sets:

238, 246, 290, 322, 406, 426, 430, 474, 498, 518, 530, 658, 670, 782, 894, 902, 1002, 1074, 1102, 1146, 1162, 1222, 1246, 1258, 1266, 1342, 1398, 1406, 1506, 1510, 1542, 1578, 1758, 1842, 1866, 1958, 1986, 2022, 2118, 2158, 2198, 2330, 2338, 2410, 2422, 2454, 2482, 2514, 2586, 2726, 2758, 2766, 2774, 2874, 2914, 2922, 2946, 2994, 3018, 3126, 3246, 3266, 3278, 3378, 3406, 3422, 3454, 3538, 3590, 3642, 3670, 3682, 3786, 3818, 3842, 3954, 3982, 4062, 4098, 4190, 4206, 4238, 4318, 4382, 4402, 4430, 4462, 4490, 4498, 4506, 4614, 4630, 4718, 4738, 4782, 4838, 4854, 4886, 4898, 4926, 4942, 4962, 4982, 5030, 5034, 5126, 5138, 5142, 5178, 5222, 5286, 5302, 5322, 5470, 5514, 5542, 5614, 5798, 5918, 5966, 6142, 6186, 6190, 6234, 6254, 6262, 6294, 6298, 6310, 6366, 6386, 6410, 6478, 6538, 6546, 6562, 6698, 6774, 6818, 6838, 6878, 6906, 7010, 7126, 7158, 7198, 7202, 7206, 7282, 7302, 7366, 7374, 7422, 7486, 7554, 7582, 7598, 7658, 7662, 7734, 7782, 7798, 7962, 7970, 8066, 8078, 8110, 8138, 8166, 8202, 8206, 8218, 8242, 8326, 8342, 8362, 8394, 8558, 8562, 8606, 8634, 8638, 8662, 8706, 8770, 8826, 8830, 8858, 8886, 8906, 8922, 8998, 9022, 9066, 9074, 9218, 9238, 9318, 9354, 9362, 9402, 9538, 9638, 9642, 9686, 9706, 9714, 9822, 9958, 10002, 10054, 10066, 10130, 10158, 10190, 10210, 10222, 10258, 10310, 10326, 10366, 10398, 10446, 10526, 10554, 10622, 10662, 10718, 10722, 10766, 10778, 10822, 10930, 10946, 10978, 11078, 11082, 11166, 11202, 11226, 11230, 11234, 11266, 11326, 11342, 11406, 11442, 11458, 11462, 11478, 11510, 11542, 11586, 11606, 11630, 11666, 11694, 11710, 11818, 11838, 11902, 11918, 11966, 11998, 12002, 12082, 12130, 12142, 12234, 12238, 12310, 12318, 12358, 12418, 12486, 12522, 12562, 12566, 12594, 12626.

Some larger examples :