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hoax n.  and  interprime n.

First numbers that belong to both sets:

160, 274, 483, 645, 650, 660, 855, 861, 915, 1344, 1404, 1581, 1665, 1795, 2541, 2640, 2751, 2760, 2826, 2960, 3285, 3345, 3381, 3390, 3505, 3552, 3615, 3694, 3736, 3930, 4024, 4054, 4189, 4344, 4460, 4564, 4594, 4676, 4824, 4954, 4980, 5022, 5068, 5150, 5425, 5652, 5742, 5854, 5874, 5946, 6060, 6260, 6356, 6364, 6603, 6702, 6714, 6960, 6980, 7212, 7268, 7402, 7503, 7978, 8014, 8084, 8091, 8164, 8185, 8214, 8292, 8421, 8673, 9193, 9330, 9346, 9630, 10179, 10604, 10689, 11679, 12612, 12650, 12795, 12847, 12932, 12956, 13096, 13419, 13506, 13518, 13560, 13616, 13761, 14076, 14484, 14715, 14998, 15024, 15126, 15144, 15282, 15764, 15780, 15813, 16735, 17050, 17148, 17175, 17324, 17616, 18069, 18278, 18360, 18454, 19080, 19084, 19590, 19606, 19761, 20578, 20596, 21273, 21615, 21667, 22117, 22386, 22444, 22475, 22558, 22983, 23163, 23750, 23764, 24549, 25092, 25177, 25245, 26256, 26295, 26420, 26637, 26682, 26734, 27247, 27382, 27418, 27540, 27546, 27820, 28104, 28182, 28620, 28662, 28905, 29150, 30138, 30390, 30397, 30523, 30834, 31693, 31746, 31986, 32118, 32197, 32562, 32793, 34048, 34152, 34264, 34640, 34725, 34972, 35145, 35239, 35358, 35756, 35806, 35874, 35928, 36015, 36535, 36555, 37165, 37176, 37359, 37374, 37812, 37822, 38116, 38160, 38225, 38238, 38250, 38460, 38758, 38965, 39307, 40234, 40477, 40587, 40594, 40944, 41208, 41250, 41275, 41600, 42184, 42435, 42495, 42825, 42834, 43287, 43484, 43680, 43737, 43947, 44056, 44145, 44268, 44525, 44532, 44619, 44775, 45069, 45180, 45186, 45333, 45436, 45594, 45650, 46318, 46563, 46590, 47029, 47155, 47328, 47358, 47425, 47700, 48020, 48120, 48425, 48793, 48858, 48950, 49040, 49200, 49302, 49351, 49423, 49924, 50926, 51424, 51846, 51945, 52278, 52296, 52366, 52618, 52635, 52716, 53181, 53428, 53595, 53626, 53725, 53884, 54006, 54054, 54369, 54553, 54582, 54814, 54873, 55606, 55977, 56047, 57232.

Some larger examples :