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Chen prime  and  nialpdrome

First numbers that belong to both sets:

2, 3, 5, 7, 11, 31, 41, 53, 71, 83, 211, 311, 431, 443, 521, 541, 631, 641, 653, 743, 751, 761, 811, 821, 863, 877, 881, 887, 911, 941, 953, 971, 977, 983, 991, 2111, 3221, 4211, 4421, 4441, 5431, 5441, 5531, 6311, 6421, 6521, 6551, 6661, 7211, 7321, 7331, 7433, 7541, 8221, 8543, 8663, 8741, 8861, 8887, 9221, 9311, 9431, 9521, 9533, 9551, 9661, 9743, 9811, 9851, 9941, 33211, 33311, 42221, 43331, 44111, 44221, 54311, 54443, 55331, 55441, 55511, 55541, 63311, 65521, 65543, 65551, 66221, 66431, 66653, 72211, 72221, 73331, 74411, 75431, 75511, 75521, 75533, 76421, 76511, 76541, 76631, 77521, 77711, 84221, 84431, 84443, 85331, 86111, 86311, 86531, 87221, 87443, 87641, 87751, 88211, 88643, 88661, 88741, 88811, 92111, 94441, 95111, 95311, 95441, 95531, 96221, 96431, 96443, 98321, 98543, 98711, 98731, 99431, 99551, 99761, 99971, 99991, 311111, 422111, 511111, 522211, 533111, 543311, 555221, 555521, 611111, 633221, 644431, 653111, 653311, 653321, 654221, 655111, 655511, 662111, 664211, 664331, 664421, 665111, 666431, 721111, 733331, 742211, 743321, 743333, 744221, 752111, 754211, 754421, 755441, 762211, 764111, 765211, 765521, 765533, 766111, 766531, 766541, 766651, 776651, 777431, 777641, 777761, 822221, 832211, 842111, 844433, 854111, 855221, 855311, 855431, 864221, 865211, 874331, 875333, 876311, 876431, 876611, 877321, 877411, 877621, 877661, 884111, 884441, 885331, 885551, 886421, 886511, 887333, 887441, 887651, 888211, 888661, 888751, 888887, 932221, 933221, 943321, 952111, 953221, 953321, 953333, 954221, 955541, 963311, 964433, 965551, 966221, 966521, 972221, 973331, 974431, 975521, 975551, 976211, 976553, 976621, 976643, 977411, 977761, 982211, 985531, 986411, 987533, 988511, 988541, 988651, 988763, 992111, 996311, 996431, 996551, 997433, 997541, 997751, 998111, 998411, 998551, 998651, 998831, 998861, 999221, 999431, 999521, 999611, 999653, 2221111, 3222211, 3222221, 3333311, 4211111, 4433333, 4443221, 4443311, 4444331, 5332211, 5333311, 5422211, 5444111, 5444321.

Some larger examples :