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plaindrome  and  prime n.

First numbers that belong to both sets:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 113, 127, 137, 139, 149, 157, 167, 179, 199, 223, 227, 229, 233, 239, 257, 269, 277, 337, 347, 349, 359, 367, 379, 389, 449, 457, 467, 479, 499, 557, 569, 577, 599, 677, 1117, 1123, 1129, 1223, 1229, 1237, 1249, 1259, 1277, 1279, 1289, 1367, 1399, 1447, 1459, 1489, 1499, 1559, 1567, 1579, 1667, 1669, 1699, 1777, 1789, 1889, 1999, 2237, 2239, 2267, 2269, 2333, 2339, 2347, 2357, 2377, 2389, 2399, 2447, 2459, 2467, 2477, 2557, 2579, 2677, 2689, 2699, 2777, 2789, 2999, 3347, 3359, 3389, 3449, 3457, 3467, 3469, 3499, 3557, 3559, 3677, 3779, 3889, 4447, 4457, 4567, 4679, 4789, 4799, 4889, 4999, 5557, 5569, 5669, 5689, 5779, 6679, 6689, 6779, 6899, 7789, 8999, 11113, 11117, 11119, 11149, 11159, 11177, 11239, 11257, 11279, 11299, 11369, 11399, 11447, 11467, 11489, 11579, 11677, 11689, 11699, 11777, 11779, 11789, 12227, 12239, 12269, 12277, 12289, 12347, 12377, 12379, 12457, 12479, 12569, 12577, 12589, 12689, 12799, 12889, 12899, 13337, 13339, 13367, 13399, 13457, 13469, 13477, 13499, 13567, 13577, 13669, 13679, 13789, 13799, 13999, 14447, 14449, 14479, 14489, 14557, 14669, 14699, 14779, 15559, 15569, 15667, 15679, 15889, 16699, 16889, 17789, 18899, 22229, 22247, 22259, 22277, 22279, 22349, 22367, 22369, 22447, 22469, 22567, 22669, 22679, 22699, 22777, 23333, 23339, 23357, 23369, 23399, 23447, 23459, 23557, 23567, 23599, 23669, 23677, 23689, 23789, 23899, 24469, 24499, 24677, 24799, 24889, 25577, 25579, 25589, 25667, 25679, 25799, 25889, 25999, 26669, 26699, 26777, 27779, 27799, 33347, 33349, 33359, 33377, 33457, 33469, 33479, 33569, 33577, 33589, 33599, 33679, 33889, 34457, 34469, 34499, 34589, 34667, 34679, 35569, 35677, 35899, 35999, 36677, 36779, 36899, 37799, 37889, 44449.

Some larger examples :