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palindromic n.  and  Sophie Germain prime

First numbers that belong to both sets:

2, 3, 5, 11, 131, 191, 12821, 14741, 19391, 19991, 36563, 38183, 93239, 96269, 1028201, 1074701, 1150511, 1178711, 1243421, 1281821, 1317131, 1333331, 1407041, 1456541, 1508051, 1532351, 1557551, 1598951, 1600061, 1609061, 1628261, 1658561, 1660661, 1688861, 1734371, 1761671, 1802081, 1832381, 1879781, 1881881, 1884881, 1958591, 1982891, 3002003, 3158513, 3193913, 3283823, 3291923, 3305033, 3365633, 3417143, 3447443, 3466643, 3589853, 3591953, 3594953, 3717173, 3763673, 3864683, 3916193, 9049409, 9169619, 9174719, 9196919, 9280829, 9477749, 9526259, 9561659, 9602069, 9758579, 9788879, 9932399, 101343101, 101424101, 101919101, 101949101, 103363301, 104787401, 106222601, 106555601, 107232701, 107757701, 108767801, 109474901, 109777901, 110343011, 111020111, 114353411, 114848411, 114878411, 115111511, 115141511, 117101711, 117323711, 117686711, 118909811, 121555121, 122262221, 122535221, 122787221, 123575321, 123767321, 124000421, 124252421, 124333421, 124525421, 125232521, 125343521, 126101621, 128070821, 128646821, 128868821, 129080921, 130030031, 134979431, 135434531, 135515531, 136090631, 136222631, 136303631, 139222931, 139282931, 139606931, 140505041, 140898041, 141242141, 141494141, 142252241, 143181341, 143262341, 145666541, 147242741, 147434741, 148666841, 148969841, 150686051, 151888151, 153404351, 154030451, 154555451, 155313551, 156434651, 156707651, 157717751, 159404951, 161535161, 161838161, 165101561, 165878561, 167787761, 167898761, 169060961, 169555961, 170232071, 170484071, 170646071, 171575171, 172393271, 172474271, 172747271, 175555571, 177323771, 181666181, 181888181, 182373281, 182949281, 184303481, 186131681, 186656681, 187444781, 187525781, 187939781, 190777091, 190909091, 191292191, 191313191, 193303391, 194292491, 196000691, 197868791, 197898791, 197919791, 300080003, 300101003, 300656003, 300929003, 302646203, 303878303, 304282403, 304414403, 307171703, 307696703, 308454803, 309515903, 310282013, 312050213, 312929213, 314646413, 315656513, 315959513, 316696613, 317646713, 317808713, 318707813, 319393913, 319999913, 320292023, 320565023, 321848123, 322030223, 324353423, 325060523, 325363523, 325636523, 327050723, 327272723, 327353723, 328030823, 330212033, 330707033, 332424233, 332484233, 333080333, 333434333, 334282433, 334777433, 336272633, 336494633, 337939733, 338343833, 338787833, 338838833, 339080933, 339878933, 343696343, 344949443, 345191543, 345494543, 345656543, 345686543, 347010743, 348959843, 349444943, 349777943, 350454053, 350868053, 350979053, 351656153, 352141253, 352909253, 354050453, 354848453, 355585553, 355909553, 355939553, 356070653, 356373653, 358747853, 359121953, 359898953, 360575063, 360818063, 364636463, 366575663, 367141763, 368040863, 369686963, 370777073, 370858073, 371424173, 371595173, 374040473, 379525973, 380979083, 381464183, 381989183, 383121383, 383979383, 385606583, 388222883.

Some larger examples :