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emirp  and  plaindrome

First numbers that belong to both sets:

13, 17, 37, 79, 113, 149, 157, 167, 179, 199, 337, 347, 359, 389, 1223, 1229, 1237, 1249, 1259, 1279, 1399, 1499, 1559, 1669, 1789, 3347, 3359, 3389, 3467, 3469, 3889, 11149, 11159, 11257, 11447, 11489, 11579, 11677, 11699, 11777, 11779, 11789, 12227, 12269, 12289, 12577, 12689, 12799, 13337, 13457, 13469, 13477, 13499, 13789, 14447, 14449, 14479, 14557, 15667, 15679, 16699, 18899, 33589, 34469, 34589, 35569, 37889, 77899, 78889, 111119, 111127, 111337, 111347, 111467, 111667, 111799, 112237, 112247, 112289, 112559, 113557, 113899, 114479, 114679, 114689, 117889, 122279, 122347, 122777, 123379, 123499, 123667, 124489, 124777, 125669, 133337, 133379, 133999, 134669, 134699, 134777, 134999, 135589, 135599, 136999, 137777, 138899, 139999, 144577, 145777, 145799, 146777, 147799, 155557, 155569, 155579, 155599, 155699, 155777, 156677, 156799, 156899, 157799, 166669, 167777, 167779, 168899, 333337, 333457, 333667, 334777, 335567, 335689, 336689, 336899, 344479, 344599, 345689, 347899, 355679, 355799, 356999, 358999, 367889, 377999, 389999, 1111339, 1111447, 1111457, 1111559, 1111577, 1111667, 1112339, 1112369, 1112389, 1112467, 1112567, 1112789, 1113349, 1115899, 1122367, 1122449, 1122899, 1123379, 1123567, 1123667, 1123777, 1125557, 1125679, 1126889, 1126999, 1128899, 1133333, 1133459, 1133479, 1133677, 1133689, 1134557, 1134667, 1135699, 1136669, 1145689, 1145999, 1155689, 1156699, 1157899, 1167889, 1222777, 1223357, 1223447, 1223689, 1224677, 1226677, 1229999, 1233377, 1233577, 1234577, 1235789, 1238999, 1245557, 1247777, 1255559, 1255567, 1258889, 1266677, 1267999, 1278899, 1333777, 1333799, 1334569, 1337779, 1344457, 1344559, 1344589, 1344799, 1344899, 1345667, 1399999, 1444447, 1444477, 1444567, 1444789, 1444999, 1445599, 1445669, 1446779, 1447889, 1455599, 1456799, 1467889, 1478999, 1556669, 1566779, 1667779, 1668889, 1678889, 1799999, 3334559, 3334999, 3335999, 3337889, 3345679, 3349999, 3355699, 3355777, 3356699, 3357899, 3358889, 3367789, 3368899, 3378889, 3444569, 3444577, 3444799, 3445567, 3445789, 3448889, 3456667, 3457777, 3458999, 3467999, 3499999, 3555677, 3555779, 3777779, 7888999, 11111117, 11111677, 11111777, 11112239, 11112259, 11113477, 11114489, 11122333, 11124569, 11124889, 11134477, 11134499, 11134777, 11134789.

Some larger examples :