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nialpdrome  and  prime n.

First numbers that belong to both sets:

2, 3, 5, 7, 11, 31, 41, 43, 53, 61, 71, 73, 83, 97, 211, 311, 331, 421, 431, 433, 443, 521, 541, 631, 641, 643, 653, 661, 733, 743, 751, 761, 773, 811, 821, 853, 863, 877, 881, 883, 887, 911, 941, 953, 971, 977, 983, 991, 997, 2111, 2221, 3221, 3331, 4111, 4211, 4421, 4441, 5333, 5431, 5441, 5443, 5521, 5531, 6211, 6221, 6311, 6421, 6521, 6551, 6553, 6653, 6661, 7211, 7321, 7331, 7333, 7411, 7433, 7541, 7621, 7643, 7741, 7753, 8111, 8221, 8311, 8431, 8443, 8521, 8543, 8641, 8663, 8731, 8741, 8753, 8761, 8821, 8831, 8861, 8863, 8887, 9221, 9311, 9421, 9431, 9433, 9511, 9521, 9533, 9551, 9631, 9643, 9661, 9721, 9733, 9743, 9811, 9833, 9851, 9871, 9883, 9887, 9931, 9941, 9973, 22111, 33211, 33311, 33331, 42221, 43321, 43331, 44111, 44221, 54311, 54331, 54421, 54443, 55331, 55333, 55411, 55441, 55511, 55541, 63211, 63311, 63331, 64333, 64433, 65111, 65521, 65543, 65551, 66221, 66431, 66533, 66541, 66553, 66643, 66653, 72211, 72221, 73331, 74311, 74411, 74441, 75211, 75431, 75511, 75521, 75533, 75541, 75553, 76333, 76421, 76441, 76511, 76541, 76543, 76631, 76651, 77431, 77521, 77543, 77551, 77611, 77621, 77641, 77711, 77731, 77743, 77761, 77773, 83221, 83311, 84211, 84221, 84421, 84431, 84443, 85331, 85333, 85411, 85531, 86111, 86311, 86441, 86531, 86533, 87211, 87221, 87421, 87433, 87443, 87511, 87541, 87553, 87631, 87641, 87643, 87721, 87743, 87751, 88211, 88321, 88411, 88643, 88651, 88661, 88663, 88721, 88741, 88771, 88811, 88843, 88853, 88861, 88873, 88883, 92111, 92221, 94111, 94321, 94331, 94421, 94433, 94441, 95111, 95311, 95441, 95443, 95531, 96211, 96221, 96331, 96431, 96443, 96553, 96643, 96661, 97441, 97511, 97553, 97651, 97711, 97771, 97777, 98221, 98321, 98411, 98443, 98533, 98543, 98621, 98641, 98663, 98711, 98731, 98773, 98873.

Some larger examples :