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centered triangular n.  and  unprimeable n.

First numbers that belong to both sets:

514, 1135, 1684, 2584, 3244, 5134, 5674, 6436, 10966, 11224, 12835, 13114, 14260, 18985, 19324, 24385, 27136, 28360, 30034, 33976, 35344, 37684, 39124, 41584, 45154, 49960, 63964, 64585, 71614, 74260, 76276, 76954, 77635, 79006, 81784, 84610, 85324, 91885, 96394, 102574, 103360, 111385, 119710, 129214, 137260, 140914, 146485, 147424, 152164, 159904, 166834, 167836, 170860, 181135, 183226, 186385, 188506, 196024, 201484, 202585, 205906, 210376, 213760, 218314, 225235, 231085, 232264, 233446, 247864, 262714, 272854, 299044, 300385, 307135, 315334, 325036, 342010, 343444, 347764, 356485, 360886, 365314, 371260, 390916, 395524, 439834, 449635, 459544, 466210, 479686, 483085, 500260, 515974, 528364, 542704, 557236, 564574, 579394, 588754, 590635, 600085, 611524, 617284, 619210, 628885, 640594, 648460, 650434, 666334, 668335, 696664, 721414, 740260, 750835, 757216, 772210, 774364, 791704, 807034, 818074, 824734, 844876, 860710, 869824, 872110, 881284, 883585, 888196, 897454, 916114, 927874, 930235, 942085, 946846, 973246, 978085, 985366, 992674, 1012294, 1024654, 1039585, 1062184, 1064710, 1077385, 1082476, 1090135, 1092694, 1113274, 1115860, 1126234, 1128835, 1141885, 1144504, 1165564, 1168210, 1178824, 1181485, 1194835, 1197514, 1210954, 1219054, 1235335, 1240786, 1248985, 1273744, 1290385, 1304335, 1307134, 1318360, 1346635, 1352326, 1355176, 1363744, 1386724, 1389610, 1404085, 1412806, 1418635, 1421554, 1433260, 1436194, 1445014, 1456816, 1495504, 1507510, 1537735, 1540774, 1580554, 1583635, 1592896, 1627084, 1630210, 1645885, 1661635, 1680634, 1690174, 1706134, 1718956, 1728604, 1744744, 1757710, 1770724, 1773985, 1823260, 1833196, 1856485, 1863166, 1876564, 1886644, 1927234, 1940860, 1944274, 1957960, 1992385, 2037586, 2041084, 2044585, 2062135, 2065654, 2069176, 2093914, 2108116, 2133085, 2140246, 2154604, 2165404, 2169010, 2179846, 2183464, 2187085, 2208874, 2227114, 2241760, 2256454, 2260135, 2271196, 2278585, 2297110, 2300824, 2311984, 2315710, 2334385, 2345626, 2353135, 2375734, 2387074, 2390860, 2406034, 2432704, 2505835, 2509714, 2540854, 2583985, 2587924, 2591866, 2607664, 2619544, 2623510, 2663335, 2667334, 2687374, 2699434, 2719594, 2723635, 2735776, 2743885, 2805085, 2817406, 2833876, 2846260, 2850394, 2862814, 2887735, 2933704, 2946304, 2963146, 2971585, 2996974, 3035260, 3065206.

Some larger examples :