Search a number
unprimeable n.  and  untouchable n.

First numbers that belong to both sets:

206, 322, 324, 326, 516, 518, 530, 624, 626, 628, 848, 892, 894, 896, 898, 1074, 1078, 1134, 1146, 1148, 1266, 1332, 1342, 1346, 1348, 1418, 1506, 1508, 1642, 1680, 1682, 1716, 1718, 1766, 1852, 1894, 1896, 1920, 1922, 1960, 1962, 2048, 2078, 2108, 2190, 2196, 2198, 2322, 2324, 2364, 2366, 2404, 2408, 2482, 2484, 2490, 2496, 2498, 2514, 2518, 2564, 2568, 2586, 2588, 2824, 2828, 2944, 2946, 2982, 2984, 3142, 3144, 3152, 3156, 3174, 3234, 3236, 3238, 3246, 3266, 3420, 3422, 3428, 3476, 3484, 3486, 3488, 3504, 3506, 3564, 3666, 3682, 3684, 3744, 3746, 3748, 3752, 3758, 3786, 3788, 3812, 3816, 3818, 3954, 3958, 3972, 3974, 4032, 4036, 4062, 4068, 4086, 4088, 4104, 4148, 4168, 4184, 4188, 4190, 4198, 4302, 4304, 4308, 4312, 4316, 4318, 4380, 4382, 4386, 4388, 4416, 4430, 4472, 4476, 4530, 4534, 4574, 4612, 4614, 4618, 4686, 4688, 4710, 4712, 4718, 4740, 4742, 4748, 4764, 4770, 4772, 4840, 4842, 4850, 4854, 4856, 4896, 4898, 4926, 4928, 5044, 5126, 5132, 5136, 5138, 5214, 5218, 5250, 5252, 5256, 5316, 5360, 5364, 5366, 5372, 5376, 5378, 5428, 5456, 5458, 5490, 5492, 5542, 5544, 5602, 5604, 5606, 5610, 5614, 5616, 5722, 5724, 5758, 5760, 5766, 5768, 5912, 5916, 5918, 5966, 5972, 6180, 6184, 6186, 6188, 6234, 6236, 6402, 6406, 6410, 6416, 6502, 6510, 6514, 6516, 6536, 6538, 6624, 6626, 6642, 6726, 6728, 6752, 6816, 6818, 6926, 7088, 7092, 7140, 7142, 7144, 7146, 7164, 7166, 7168, 7260, 7266, 7272, 7316, 7374, 7376, 7380, 7382, 7388, 7400, 7402, 7406, 7422, 7424, 7428, 7444, 7446, 7466, 7468, 7612, 7614, 7616, 7658, 7732, 7734, 7764, 7768, 7770, 7772, 7774, 7890, 7892, 7970, 7972, 7976, 7988, 8024, 8028, 8046, 8048, 8078, 8130, 8136, 8138, 8152.

Some larger examples :