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interprime n.  and  pancake n.

First numbers that belong to both sets:

4, 56, 154, 254, 436, 596, 667, 1036, 1226, 4096, 5566, 9046, 11477, 11936, 16654, 16837, 18146, 19504, 36316, 45754, 56954, 63904, 65704, 68636, 76246, 85906, 95704, 108812, 120296, 153736, 174937, 193754, 210926, 232904, 246754, 247457, 255256, 257404, 266086, 275654, 277886, 290704, 311656, 318004, 323611, 364232, 371954, 373681, 392056, 402754, 431057, 443212, 449827, 458404, 485606, 490546, 497504, 502504, 509546, 529936, 552827, 627761, 631127, 652654, 688552, 699154, 709837, 725411, 739937, 775636, 788141, 794431, 804547, 807086, 812176, 816004, 819841, 821122, 877151, 915982, 929567, 972316, 991937, 1000406, 1004654, 1041847, 1087076, 1107817, 1125751, 1159004, 1231666, 1239526, 1250572, 1276004, 1316254, 1340704, 1420456, 1427206, 1428896, 1435666, 1456072, 1499047, 1537382, 1565566, 1567336, 1599367, 1602946, 1624504, 1640767, 1697404, 1723297, 1747516, 1749386, 1785106, 1809754, 1823096, 1838404, 1849927, 1859557, 1985029, 1993007, 2029106, 2089991, 2094082, 2098177, 2102276, 2158004, 2193466, 2216566, 2312326, 2327404, 2355536, 2381654, 2427707, 2429911, 2432116, 2650754, 2669206, 2685404, 2703976, 2713286, 2778904, 2812007, 2845306, 2917321, 2975581, 3029492, 3201716, 3288331, 3301166, 3311452, 3402137, 3539131, 3576476, 3595222, 3597904, 3635557, 3692404, 3771632, 3818467, 3832297, 3851701, 3854477, 3918601, 3949456, 4003036, 4128502, 4220966, 4226779, 4270504, 4364536, 4388204, 4423826, 4429777, 4495502, 4564732, 4753987, 4787966, 4840717, 4959676, 5013362, 5083267, 5279626, 5302397, 5308912, 5335012, 5463166, 5562781, 5626336, 5703754, 5774902, 5791907, 5832821, 5870452, 5925404, 6067387, 6074356, 6320791, 6327904, 6431492, 6663076, 6688654, 6699631, 6732616, 6809896, 6813587, 6824666, 6917341, 6947129, 7006897, 7014386, 7025627, 7081967, 7104566, 7282837, 7305754, 7363204, 7533022, 7740146, 7850704, 7994002, 7998001, 8034037, 8042056, 8170904, 8215432, 8333404, 8613326, 8750837, 9178471, 9476482, 9638246, 9686602, 9779254, 9814666, 9832396, 9934654, 10010576, 10253657, 10271779, 10348976, 10353526, 10408204, 10431029, 10472177, 10536346, 10568504, 10591504, 10605316, 10642192, 10656037, 10962904, 11000396, 11014472, 11047351, 11113256, 11122687, 11141561, 11160451, 11245654, 11302636, 11359762, 11378836, 11498411, 11623432, 11662036, 11700704, 11715221, 11978066, 12036872, 12056506, 12115504, 12224041, 12253726, 12298321, 12432592, 12552556, 12607732, 12673096, 12849916.

Some larger examples :