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de Polignac n.  and  plaindrome

First numbers that belong to both sets:

1, 127, 149, 337, 599, 1199, 1259, 1477, 1589, 1777, 2279, 2377, 2579, 2669, 2789, 2999, 3779, 4567, 4589, 4889, 5557, 7799, 11137, 11227, 11239, 11279, 11335, 11347, 11579, 11789, 12223, 12233, 12239, 12479, 13469, 13589, 13679, 13799, 14459, 14467, 14489, 15779, 18889, 18899, 22567, 23339, 23669, 24467, 24557, 24569, 24577, 24599, 24889, 24899, 25777, 25799, 26789, 26999, 33389, 33449, 33667, 33689, 33699, 34457, 34679, 34889, 35699, 36667, 36677, 38999, 44489, 44669, 45579, 45899, 55559, 55777, 55799, 56669, 57779, 57899, 58889, 66667, 111133, 111139, 111239, 111367, 111449, 111457, 111599, 111679, 111779, 111899, 112237, 112247, 112337, 112349, 112447, 112449, 112457, 112499, 112555, 113347, 113369, 113377, 113467, 113477, 113579, 113669, 113789, 114479, 114577, 114689, 114779, 116999, 122377, 122399, 122467, 122489, 122557, 123335, 123359, 123667, 124489, 124567, 124667, 124679, 125579, 125789, 126667, 126779, 126799, 127799, 133349, 133667, 133679, 134489, 134569, 134669, 135569, 135599, 135667, 135779, 135899, 144449, 144457, 145589, 146789, 147779, 147899, 155677, 156899, 166679, 166889, 167999, 222389, 222599, 222689, 223379, 223589, 224789, 225667, 225689, 225899, 233459, 233669, 233899, 234455, 234569, 234899, 235777, 238889, 239999, 244477, 244799, 245557, 246689, 246999, 248999, 255557, 255577, 255689, 255899, 256799, 257779, 257789, 266669, 269999, 277799, 277999, 333479, 334469, 334499, 334567, 335799, 336689, 336779, 338999, 344459, 344467, 344579, 344677, 345569, 345599, 346679, 348889, 355679, 356669, 356999, 357779, 358889, 359999, 366667, 367799, 367889, 367999, 388889, 444449, 444689, 445559, 445567, 445679, 445789, 446699, 446779, 447779, 449999, 455669, 455677, 455789, 456689, 456899, 457777, 457889, 458999, 459999, 466799, 466889, 477899, 499999, 555689, 555899, 567779, 577777, 577799, 578999, 588899, 666779, 667799, 667889, 668999, 689999, 788999, 1111117, 1111133, 1111147, 1111289, 1111379, 1112227, 1112249, 1113379, 1113457, 1113479, 1113679, 1113689, 1115677, 1116799, 1116899, 1122239, 1122247, 1122335, 1122377, 1122449, 1122479, 1122599, 1122689, 1123333, 1123379, 1123457, 1123469, 1123579.

Some larger examples :