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katadrome  and  unprimeable n.

First numbers that belong to both sets:

320, 510, 530, 532, 620, 840, 842, 4310, 5210, 5310, 5420, 6410, 6430, 6432, 6510, 6530, 6532, 7310, 7420, 7610, 7650, 7652, 7654, 8610, 8630, 8632, 8650, 8652, 8654, 8720, 9210, 9650, 9652, 9654, 9750, 9752, 9754, 9840, 9842, 9860, 9862, 9864, 9865, 43210, 53210, 65310, 73210, 75310, 75410, 75420, 76310, 76320, 76410, 76430, 76432, 76520, 84320, 85320, 86210, 86430, 86432, 86510, 86520, 86540, 86542, 87410, 87650, 87652, 87654, 93210, 94310, 95430, 95432, 96310, 96420, 96530, 96532, 96540, 96542, 97310, 97410, 97430, 97432, 97530, 97532, 97620, 97630, 97632, 98430, 98432, 98520, 98610, 98650, 98652, 98654, 98740, 98742, 98750, 98752, 98754, 98760, 98762, 98764, 98765, 653210, 654210, 654310, 743210, 753210, 754310, 754320, 763210, 764210, 765410, 765420, 854310, 863210, 865410, 865420, 865430, 865432, 873210, 874310, 874320, 875430, 875432, 876210, 876410, 876420, 876510, 876530, 876532, 876540, 876542, 953210, 954210, 964310, 964320, 965210, 965430, 965432, 975410, 976310, 976320, 976420, 976520, 976540, 976542, 983210, 984310, 985310, 985320, 985420, 986310, 986320, 986520, 987320, 987410, 987420, 987510, 987610, 987620, 987640, 987642, 6543210, 7654320, 8543210, 8654210, 8654310, 8654320, 8754210, 8754320, 8763210, 8764210, 8765210, 8765310, 9543210, 9654210, 9654310, 9753210, 9764320, 9765310, 9765410, 9765420, 9853210, 9854310, 9863210, 9864210, 9864310, 9864320, 9865310, 9865320, 9865420, 9873210, 9874210, 9875210, 9875310, 9875430, 9875432, 9876210, 9876310, 9876320, 9876420, 9876530, 9876532, 9876540, 9876542.