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balanced n.  and  unprimeable n.

First numbers that belong to both sets:

204, 518, 532, 534, 535, 620, 622, 624, 625, 626, 628, 842, 844, 894, 898, 1070, 1138, 1142, 1334, 1346, 1358, 1646, 1670, 1766, 1790, 1922, 2070, 2102, 2362, 2364, 2402, 2405, 2406, 2482, 2484, 2488, 2514, 2516, 2566, 2582, 2586, 2826, 2980, 2984, 3095, 3150, 3155, 3158, 3174, 3178, 3235, 3238, 3242, 3244, 3282, 3284, 3288, 3425, 3426, 3428, 3474, 3476, 3480, 3504, 3660, 3665, 3666, 3668, 3682, 3684, 3688, 3745, 3746, 3748, 3752, 3780, 3784, 3970, 3972, 3976, 4032, 7115, 7145, 7275, 7445, 7835, 8135, 8255, 8335, 8345, 8495, 8555, 8558, 8615, 8630, 8634, 8636, 8654, 8795, 8798, 8855, 8875, 8878, 8910, 8915, 8918, 8980, 8985, 9035, 9038, 9074, 9076, 9080, 9110, 9114, 9116, 9140, 9144, 9445, 9446, 9450, 9452, 9458, 9502, 9562, 9564, 9574, 9578, 9592, 9650, 9652, 9656, 9700, 9704, 9755, 9758, 9774, 9842, 9844, 9848, 9894, 9898, 9912, 9954, 9956, 9995, 9998, 10010, 10012, 10022, 10025, 10026, 10028, 10040, 10054, 10058, 10082, 10084, 10088, 10122, 10124, 10208, 10295, 10375, 10414, 10445, 10446, 10542, 10545, 10570, 10574, 10575, 10645, 10646, 10674, 10676, 10805, 10806, 10810, 10812, 10872, 10915, 10918, 10922, 10924, 10962, 10964, 10968, 11015, 11030, 11034, 11036, 11105, 11106, 11108, 11120, 11184, 11200, 11202, 11204, 11208, 11220, 11225, 11335, 11342, 11345, 11370, 11372, 11378, 11405, 11406, 11455, 11534, 11535, 11560, 11562, 11564, 11565, 11602, 11604, 11608, 11660, 11665, 11666, 11668, 11720, 11725, 11728, 11765, 11790, 11795, 11798, 11840, 11845, 11846, 11850, 11852, 11855, 11858, 11870, 11874, 11876, 11910, 11914, 11915, 11916, 12050, 12052, 12056, 12065, 12066, 12068, 12080, 12125, 12128, 12130, 12176, 12315, 12335, 12350, 12382, 12445, 12446, 12462, 12590, 12595, 12598, 12622, 12660, 12664, 12665, 12770, 12772, 12776, 12815, 12830, 12860, 12875, 12878, 12935.

Some larger examples :