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Chen prime  and  plaindrome

First numbers that belong to both sets:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 59, 67, 89, 113, 127, 137, 139, 149, 157, 167, 179, 199, 227, 233, 239, 257, 269, 337, 347, 359, 379, 389, 449, 467, 479, 499, 557, 569, 577, 599, 677, 1117, 1229, 1259, 1277, 1289, 1367, 1399, 1459, 1499, 1559, 1567, 1667, 1669, 1777, 1889, 2237, 2267, 2269, 2333, 2339, 2357, 2389, 2447, 2459, 2467, 2477, 2557, 2579, 2699, 2777, 2789, 2999, 3347, 3359, 3389, 3457, 3467, 3557, 3559, 3677, 3779, 3889, 4447, 4567, 4679, 4789, 4799, 4889, 4999, 5669, 6689, 6779, 6899, 8999, 11117, 11159, 11177, 11279, 11299, 11369, 11399, 11447, 11467, 11489, 11579, 11699, 11777, 11789, 12227, 12239, 12269, 12277, 12347, 12377, 12379, 12457, 12479, 12569, 12889, 13337, 13339, 13367, 13457, 13469, 13477, 13499, 13567, 13577, 13679, 13789, 13799, 14447, 14449, 14489, 14669, 14699, 15569, 15679, 15889, 17789, 18899, 22247, 22259, 22277, 22367, 22369, 22469, 22567, 22679, 23339, 23369, 23399, 23447, 23459, 23557, 23599, 23669, 23789, 24499, 24889, 25577, 25579, 25589, 25679, 25799, 25889, 26669, 26699, 26777, 27779, 33347, 33349, 33359, 33377, 33479, 33569, 33589, 33599, 34457, 34469, 34499, 34589, 34667, 34679, 36677, 36779, 36899, 37799, 37889, 44579, 44699, 44777, 44789, 45557, 45569, 45599, 45677, 45779, 46679, 46889, 47777, 55589, 55667, 55799, 55889, 57899, 59999, 78889, 111119, 111149, 111227, 111269, 111347, 111667, 111779, 112247, 112289, 112337, 112339, 112349, 112559, 112577, 112799, 113357, 113557, 113567, 113777, 113899, 114467, 114479, 114599, 114689, 115679, 115777, 116789, 117779, 117899, 122267, 122279, 122399, 122477, 122489, 122557, 122579, 122599, 122777, 123377, 123449, 123677, 124679, 124777, 124799, 125777, 125789, 133337, 133349, 133379, 133447, 133499, 133559, 134489, 134669, 134677, 134777, 134789, 134999, 135589, 135599, 135899, 136889, 136999, 137777, 137999, 138899, 144479, 144577, 144589.

Some larger examples :