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apocalyptic n.  and  interprime n.

First numbers that belong to both sets:

192, 312, 506, 582, 610, 650, 660, 667, 714, 723, 747, 822, 828, 846, 861, 882, 924, 994, 1026, 1056, 1062, 1092, 1140, 1158, 1230, 1243, 1281, 1286, 1290, 1305, 1416, 1449, 1452, 1465, 1482, 1485, 1488, 1527, 1546, 1556, 1590, 1611, 1665, 1695, 1715, 1722, 1744, 1750, 1785, 1806, 1817, 1827, 1839, 1864, 1884, 1895, 1910, 1990, 2001, 2007, 2034, 2066, 2105, 2130, 2134, 2148, 2157, 2170, 2210, 2229, 2238, 2247, 2259, 2271, 2277, 2284, 2290, 2303, 2310, 2322, 2340, 2344, 2349, 2364, 2382, 2386, 2396, 2414, 2430, 2470, 2490, 2546, 2550, 2627, 2674, 2680, 2691, 2703, 2709, 2716, 2724, 2730, 2736, 2751, 2760, 2794, 2826, 2835, 2847, 2854, 2859, 2870, 2883, 2900, 2906, 2933, 2946, 2955, 2960, 2966, 2985, 3000, 3021, 3039, 3055, 3064, 3073, 3081, 3120, 3129, 3150, 3165, 3175, 3184, 3189, 3197, 3213, 3219, 3225, 3258, 3265, 3285, 3300, 3304, 3310, 3316, 3321, 3326, 3330, 3366, 3381, 3390, 3441, 3459, 3462, 3465, 3480, 3495, 3522, 3528, 3531, 3536, 3540, 3552, 3576, 3588, 3610, 3615, 3620, 3651, 3672, 3675, 3684, 3699, 3705, 3714, 3730, 3736, 3750, 3768, 3774, 3786, 3795, 3800, 3828, 3840, 3858, 3879, 3885, 3898, 3921, 3930, 3937, 3945, 3957, 3978, 3995, 4002, 4010, 4020, 4054, 4076, 4085, 4092, 4105, 4119, 4128, 4136, 4146, 4155, 4189, 4206, 4214, 4218, 4242, 4256, 4260, 4272, 4278, 4286, 4312, 4344, 4368, 4382, 4394, 4415, 4422, 4449, 4454, 4460, 4488, 4510, 4515, 4535, 4548, 4555, 4587, 4594, 4612, 4629, 4638, 4641, 4650, 4654, 4660, 4668, 4676, 4685, 4697, 4712, 4722, 4726, 4742, 4755, 4771, 4785, 4788, 4791, 4796, 4800, 4807, 4846, 4866, 4874, 4883, 4896, 4914, 4925, 4935, 4947, 4954, 4962, 4968, 4971, 4980, 5006, 5010, 5022, 5055, 5068.

Some larger examples :