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palindromic n.  and  unprimeable n.

First numbers that belong to both sets:

515, 535, 626, 848, 898, 4554, 4774, 5995, 8338, 8558, 20302, 20602, 21112, 22322, 22422, 22522, 22822, 23232, 23732, 23932, 24142, 24342, 24642, 25552, 25852, 26062, 26362, 26462, 26762, 26962, 27372, 27572, 27872, 27972, 28482, 28582, 28882, 28982, 29092, 29492, 29692, 29792, 29892, 29992, 40104, 40204, 40304, 40404, 41314, 42124, 42424, 42524, 42624, 43434, 43534, 43734, 43834, 44144, 44344, 44944, 45154, 45354, 45454, 46164, 46364, 46464, 46964, 47074, 47174, 47374, 47474, 47574, 47674, 47874, 48084, 48684, 49094, 49794, 50305, 50405, 50605, 50805, 51015, 51115, 51315, 52425, 52825, 52925, 53035, 53135, 53335, 53535, 54145, 54245, 54745, 54845, 55155, 55555, 55655, 55755, 55855, 55955, 56065, 56865, 57475, 57875, 58085, 58285, 58385, 58585, 58985, 59295, 59595, 59895, 60006, 60306, 60406, 60806, 61016, 61116, 61316, 61916, 62026, 62226, 62526, 63236, 63636, 63936, 64046, 64146, 64246, 64346, 64446, 64546, 64646, 64946, 65156, 65456, 65756, 66266, 66666, 66966, 67176, 67376, 67876, 68186, 68786, 68986, 69096, 69296, 69396, 69796, 80008, 80508, 81218, 81318, 81418, 81718, 82328, 82628, 82828, 82928, 83038, 84548, 84748, 84848, 85058, 85358, 85558, 85658, 85958, 86668, 87378, 87578, 87778, 88088, 88188, 88388, 88488, 88988, 89098, 89198, 89698, 89998, 204402, 209902, 211112, 212212, 214412, 215512, 221122, 222222, 223322, 229922, 230032, 232232, 233332, 236632, 244442, 245542, 247742, 248842, 253352, 254452, 257752, 258852, 259952, 260062, 269962, 272272, 273372, 277772, 280082, 283382, 285582, 288882, 290092, 292292, 402204, 404404, 405504, 406604, 410014, 413314, 416614, 419914, 422224, 426624, 428824, 430034, 431134, 432234, 435534, 436634, 437734, 439934, 441144, 450054, 452254, 453354, 458854, 459954, 461164, 465564, 466664, 467764, 475574, 476674, 477774, 480084, 488884, 491194, 495594, 496694, 497794, 498894, 499994, 502205, 507705, 508805, 510015, 512215, 521125, 523325, 530035, 532235, 533335, 535535, 538835, 539935, 542245, 544445, 550055, 551155, 558855, 559955, 560065, 562265, 563365, 566665.

Some larger examples :