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pancake n.  and  prime n.

First numbers that belong to both sets:

2, 7, 11, 29, 37, 67, 79, 137, 191, 211, 277, 379, 631, 821, 947, 991, 1129, 1327, 1597, 1831, 2017, 2081, 2347, 2557, 2851, 2927, 3571, 3917, 4561, 4657, 4951, 5051, 5779, 6217, 6329, 8647, 8779, 9181, 9871, 11027, 12721, 13367, 14029, 14197, 14879, 15401, 16111, 17021, 17579, 20101, 20707, 21529, 21737, 22367, 24091, 24977, 26107, 27967, 28921, 31627, 33931, 34981, 36857, 37951, 39341, 40471, 41617, 42487, 43661, 44851, 47279, 50087, 51361, 53629, 58997, 59341, 60727, 62129, 64621, 66067, 66431, 69379, 70501, 70877, 75079, 77029, 78607, 79801, 83437, 87991, 88411, 91807, 93097, 93529, 95267, 96581, 97021, 98347, 100129, 106031, 107881, 109279, 113051, 117371, 122761, 126757, 127261, 129287, 130817, 133387, 135461, 145531, 150427, 152077, 152629, 154291, 156521, 157081, 163307, 165601, 167911, 168491, 177907, 182107, 182711, 185137, 189421, 194377, 196879, 197507, 200029, 202567, 204481, 210277, 212227, 215497, 218131, 222779, 225457, 226129, 230861, 234271, 236329, 239087, 239779, 241861, 248161, 250279, 255971, 256687, 271217, 274171, 282377, 289181, 292231, 294529, 297607, 310867, 319601, 320401, 322807, 329267, 333337, 342379, 346529, 352381, 356591, 359129, 363379, 365941, 372817, 377147, 380629, 387641, 394717, 411779, 426427, 427351, 433847, 438517, 442271, 445097, 446041, 448879, 468029, 471907, 484621, 488567, 491537, 495511, 500501, 512579, 515621, 519691, 523777, 524801, 531997, 548629, 557041, 565517, 575129, 579427, 595687, 596779, 605551, 608857, 613279, 614387, 617717, 632251, 641279, 653797, 658379, 668747, 673381, 682697, 705079, 706267, 730237, 733867, 738721, 743591, 744811, 749701, 769421, 773147, 779377, 784379, 799481, 809629, 818561, 828829, 830117, 839161, 840457, 844351, 893117, 903841, 914629, 930931, 941879, 947377, 957037, 968137, 990529, 996167, 1001821, 1008911, 1018879, 1026029, 1043291, 1049077, 1066531, 1072381, 1078247, 1090027, 1094461, 1100387, 1101871, 1118261, 1124251, 1130257, 1143829, 1149887, 1155961, 1198927, 1216021, 1222267, 1248991, 1253737, 1255321, 1272811, 1285607, 1292029, 1298467, 1337431, 1345621, 1352191, 1357129, 1363727.

Some larger examples :