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sphenic n.  and  Ulam n.

First numbers that belong to both sets:

102, 114, 138, 182, 238, 258, 273, 282, 370, 402, 429, 434, 483, 602, 627, 646, 861, 986, 1023, 1030, 1311, 1335, 1338, 1406, 1462, 1790, 1834, 1902, 1946, 2054, 2093, 2134, 2247, 2330, 2354, 2445, 2486, 2613, 2630, 2635, 2674, 2919, 2985, 3070, 3219, 3395, 3417, 3451, 3454, 3495, 3605, 3723, 3759, 3806, 3874, 3886, 3918, 3962, 4038, 4118, 4155, 4233, 4294, 4390, 4407, 4646, 5018, 5035, 5037, 5118, 5159, 5162, 5181, 5206, 5291, 5335, 5487, 5514, 5665, 5685, 5770, 5795, 5797, 5826, 5829, 5858, 5902, 5946, 6154, 6310, 6322, 6366, 6391, 6410, 6479, 6567, 6586, 6721, 6735, 6738, 6806, 6862, 7158, 7258, 7278, 7302, 7322, 7366, 7473, 7498, 7539, 7622, 7730, 7798, 7818, 7881, 8018, 8062, 8099, 8126, 8165, 8194, 8238, 8255, 8277, 8338, 8421, 8426, 8570, 8666, 8702, 8754, 8815, 8942, 8949, 9015, 9093, 9118, 9186, 9262, 9399, 9401, 9443, 9699, 9726, 9807, 9919, 9958, 10002, 10090, 10222, 10283, 10286, 10366, 10569, 10718, 10806, 10833, 10865, 10870, 10994, 11085, 11226, 11229, 11234, 11258, 11586, 11605, 11627, 11649, 11713, 11994, 12035, 12062, 12118, 12145, 12162, 12189, 12245, 12338, 12363, 12578, 12595, 12639, 12749, 12766, 12790, 12873, 12878, 12939, 13030, 13066, 13179, 13237, 13242, 13281, 13413, 13506, 13533, 13611, 13677, 13694, 13719, 13758, 13782, 13958, 14046, 14066, 14102, 14127, 14195, 14298, 14366, 14559, 14691, 14735, 14774, 14818, 14838, 14862, 14894, 14906, 14926, 15322, 15358, 15385, 15490, 15598, 15617, 15622, 15818, 15879, 15962, 16287, 16289, 16306, 16394, 16419, 16502, 16670, 16702, 16746, 16827, 16849, 16851, 16915, 17005, 17135, 17242, 17301, 17330, 17347, 17499, 17501, 17518, 17562, 17758, 17782, 17826, 17841, 17870, 17890, 17907, 17995, 17997, 18046, 18146, 18193, 18195, 18305, 18381, 18535, 18537, 18557, 18574, 18579, 18681, 18962, 19055, 19058.

Some larger examples :