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palindromic n.  and  twin primes

First numbers that belong to both sets:

3, 5, 7, 11, 101, 151, 181, 191, 313, 10301, 10501, 12821, 13831, 13931, 16061, 16361, 19891, 19991, 31513, 32323, 34843, 35053, 37573, 72227, 73037, 76367, 77477, 78887, 79397, 79697, 79997, 93239, 94349, 94649, 94849, 94949, 95959, 97379, 97579, 98389, 1003001, 1055501, 1062601, 1129211, 1134311, 1163611, 1183811, 1186811, 1193911, 1201021, 1208021, 1212121, 1221221, 1242421, 1250521, 1253521, 1262621, 1268621, 1281821, 1286821, 1362631, 1486841, 1496941, 1532351, 1535351, 1572751, 1580851, 1589851, 1598951, 1609061, 1633361, 1660661, 1685861, 1707071, 1712171, 1734371, 1748471, 1755571, 1802081, 1820281, 1842481, 1883881, 1908091, 1924291, 1963691, 1976791, 1987891, 1995991, 3001003, 3007003, 3064603, 3072703, 3091903, 3222223, 3228223, 3315133, 3329233, 3331333, 3424243, 3443443, 3449443, 3470743, 3479743, 3528253, 3569653, 3601063, 3716173, 3746473, 3858583, 3863683, 3871783, 3899983, 7041407, 7069607, 7082807, 7093907, 7118117, 7129217, 7159517, 7194917, 7257527, 7388837, 7401047, 7475747, 7489847, 7519157, 7527257, 7540457, 7600067, 7611167, 7630367, 7666667, 7715177, 7750577, 7778777, 7783877, 7868687, 7930397, 7933397, 7960697, 7977797, 9002009, 9067609, 9103019, 9174719, 9200029, 9209029, 9230329, 9231329, 9271729, 9277729, 9286829, 9318139, 9324239, 9397939, 9414149, 9440449, 9493949, 9547459, 9561659, 9624269, 9650569, 9686869, 9709079, 9724279, 9743479, 9795979, 9818189, 9845489, 9888889, 9896989, 9907099, 9918199, 9919199, 9965699, 100060001, 100111001, 100161001, 100767001, 101141101, 101414101, 101616101, 101949101, 102454201, 102838201, 103060301, 103282301, 103323301, 103515301, 103575301, 104222401, 105343501, 106444601, 106464601, 106545601, 106909601, 107636701, 107868701, 108434801, 108565801, 108686801, 109111901, 109575901, 109777901, 109818901, 110111011, 110232011, 110505011, 110747011, 111070111, 111757111, 112111211, 112212211, 112494211, 112636211, 112878211, 113565311, 113636311, 113888311, 114353411, 114818411, 115464511, 115545511, 115797511, 116010611, 116424611, 116868611, 117101711, 117262711, 117959711, 118717811, 118818811, 118959811, 119202911, 119696911, 120565021, 120868021, 120989021, 121818121, 122262221, 122333221, 123292321, 123989321, 124131421, 124656421, 124737421, 125838521, 127212721, 127636721, 127686721, 127929721, 129494921, 130464031, 130585031, 130818031, 130858031, 131030131, 131111131, 131646131, 134232431, 134858431, 134909431, 135515531, 136222631, 136818631, 137040731, 137363731, 137424731, 137636731, 138040831, 138242831, 138454831, 139161931, 139383931, 139717931, 140030041, 141484141, 141848141, 142030241, 142272241.

Some larger examples :