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interprime n.  and  palindromic n.

First numbers that belong to both sets:

4, 6, 9, 99, 111, 282, 363, 393, 414, 515, 636, 656, 696, 747, 828, 858, 909, 939, 969, 1551, 2112, 2772, 4224, 4444, 7007, 9009, 9339, 9669, 10101, 11511, 12921, 13431, 16761, 17571, 21012, 21612, 23832, 26262, 26862, 28182, 29292, 29492, 30503, 31313, 32223, 33033, 33633, 34743, 36363, 37473, 39093, 40704, 41014, 41614, 43434, 44644, 45754, 46464, 46864, 47274, 48484, 48784, 50805, 54145, 54945, 55155, 56265, 56865, 57075, 57975, 58385, 58985, 60006, 61816, 62226, 66966, 67076, 68486, 68886, 70907, 71017, 72927, 73137, 76467, 79197, 80208, 81018, 82728, 83238, 83838, 84348, 88388, 89298, 89598, 89898, 90009, 90909, 92529, 93839, 93939, 95259, 96069, 96569, 96669, 99399, 102201, 105501, 108801, 132231, 147741, 148841, 160061, 185581, 197791, 209902, 216612, 230032, 240042, 246642, 270072, 276672, 277772, 279972, 292292, 303303, 324423, 335533, 340043, 357753, 358853, 386683, 432234, 434434, 439934, 443344, 452254, 468864, 498894, 499994, 507705, 508805, 534435, 538835, 543345, 550055, 562265, 564465, 568865, 572275, 573375, 605506, 630036, 631136, 640046, 651156, 658856, 665566, 690096, 691196, 695596, 702207, 734437, 739937, 740047, 752257, 754457, 762267, 767767, 810018, 824428, 827728, 866668, 909909, 933339, 940049, 966669, 988889, 993399, 1001001, 1014101, 1023201, 1056501, 1075701, 1083801, 1096901, 1149411, 1154511, 1170711, 1176711, 1187811, 1191911, 1220221, 1225221, 1234321, 1239321, 1258521, 1266621, 1269621, 1274721, 1304031, 1331331, 1386831, 1399931, 1417141, 1438341, 1449441, 1462641, 1478741, 1503051, 1522251, 1547451, 1596951, 1626261, 1645461, 1656561, 1661661, 1675761, 1691961, 1740471, 1751571, 1762671, 1796971, 1809081, 1818181, 1828281, 1835381, 1836381, 1840481, 1854581, 1858581, 1920291, 1923291, 1926291, 1931391, 1934391, 1986891, 1991991, 1996991, 2020202, 2035302, 2038302, 2067602, 2088802, 2109012, 2136312, 2155512, 2158512, 2182812, 2199912, 2200022, 2237322, 2396932, 2422242, 2428242, 2460642, 2469642, 2479742, 2484842, 2499942, 2526252, 2528252, 2529252, 2536352, 2545452, 2561652, 2580852, 2594952, 2599952, 2601062, 2615162, 2622262, 2638362, 2657562, 2673762, 2692962, 2697962, 2726272, 2733372, 2746472, 2760672.

Some larger examples :