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interprime n.  and  pentagonal n.

First numbers that belong to both sets:

12, 176, 376, 532, 590, 3015, 4510, 4676, 7315, 7526, 7957, 8855, 12650, 15555, 17120, 19437, 20126, 22265, 25676, 29330, 30175, 40755, 48510, 54626, 78547, 82017, 91390, 97410, 101270, 102051, 102835, 105205, 108407, 119145, 148680, 151527, 153440, 198562, 200751, 206276, 210750, 214137, 243412, 245835, 254410, 266915, 279720, 283620, 299490, 338200, 351142, 352595, 355510, 364327, 373252, 377755, 392960, 408465, 413175, 427467, 446901, 451827, 456780, 485357, 487065, 502572, 528957, 532526, 559676, 572577, 576290, 581882, 631477, 653070, 699392, 734650, 768626, 790251, 812176, 836640, 866020, 875162, 886657, 898227, 926301, 950026, 957202, 959600, 962001, 993487, 1008190, 1025480, 1042917, 1047926, 1093547, 1116722, 1134915, 1140140, 1153255, 1198407, 1203776, 1209157, 1214550, 1244426, 1280202, 1333402, 1339065, 1358980, 1364697, 1402150, 1445995, 1454845, 1460760, 1478577, 1523592, 1541787, 1553977, 1615647, 1634382, 1659530, 1675345, 1684870, 1745822, 1765295, 1887765, 1938585, 2014342, 2017820, 2035255, 2042250, 2070350, 2073876, 2102192, 2105745, 2181051, 2184670, 2195545, 2199176, 2206447, 2221025, 2313225, 2358147, 2369445, 2399705, 2449287, 2495505, 2514890, 2549972, 2620865, 2640730, 2676676, 2692730, 2761495, 2794155, 2918340, 2951912, 2998387, 3002630, 3011125, 3045225, 3053780, 3135651, 3157376, 3329405, 3515176, 3524367, 3565875, 3630926, 3786587, 3877692, 3901847, 3911530, 4068090, 4157505, 4167500, 4472930, 4478112, 4493676, 4592875, 4619160, 4634967, 4671955, 4714407, 4735705, 4816000, 4907817, 5022435, 5027926, 5071962, 5088525, 5160610, 5188470, 5255640, 5306301, 5328895, 5351537, 5436872, 5482660, 5621176, 5644430, 5921260, 5969040, 5975026, 6005001, 6029035, 6235262, 6321187, 6345845, 6444957, 6451177, 6588776, 6645485, 6651801, 6683426, 6715126, 6881175, 6958497, 7042750, 7075290, 7206200, 7291935, 7498426, 7532001, 7538725, 7606130, 7626410, 7735026, 7782787, 7920057, 7947655, 7996067, 8107275, 8156170, 8163167, 8191185, 8282575, 8388655, 8417057, 8424165, 8725410, 8732647, 8761625, 8863426, 8885317, 9039310, 9172357, 9194626, 9246692, 9306376, 9441367, 9577330, 10193370, 10311015, 10389820, 10652005, 10700026, 10732100, 10788345, 11104401, 11375397, 11516276, 11549550, 11927190, 12011935, 12182325, 12199430, 12267970, 12345307, 12613550, 12700695, 12831975, 12928676, 12999232, 13025740, 13132042, 13265527, 13274450, 13292305, 13319110, 13372801.

Some larger examples :