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balanced prime  and  nialpdrome

First numbers that belong to both sets:

5, 53, 211, 653, 733, 977, 9871, 54443, 66431, 75533, 84443, 94433, 96431, 97441, 311111, 733111, 744221, 854111, 873331, 875333, 975433, 996551, 997433, 998743, 999541, 6553331, 6655321, 7441111, 7444331, 7553333, 7621111, 7653211, 7763111, 8522221, 8666431, 8773211, 8833211, 8866433, 8866621, 8884433, 9544433, 9664411, 9886211, 9999883, 42211111, 55555553, 66333221, 76544411, 76555411, 76666333, 76666643, 77544331, 77776333, 84333331, 85443331, 87322211, 87755531, 87764321, 88842211, 97665551, 97753321, 98654221, 98765333, 98854421, 98874421, 98888633, 98888731, 99543331, 99544321, 99644443, 99743321, 99744221, 99777653, 99876311, 99966631, 99975541, 99988331, 665433311, 666333221, 666533333, 666655321, 744443333, 754222211, 766666633, 774432221, 774433333, 775555511, 777632111, 777664441, 777666553, 853211111, 855332111, 864222211, 864333331, 864444433, 865432111, 866554111, 875543311, 877722221, 885311111, 885555431, 887765521, 888333331, 888844421, 888877321, 888884431, 944433331, 963331111, 966443111, 976554211, 977554411, 977774443, 985422211, 986666311, 988555333, 988644421, 988886653, 988887551, 994433333, 997666633, 997733221, 998555531, 998663333, 998766553, 999977411, 999994433, 4443311111, 5222222221, 6555311111, 6665433221, 6666432221, 7444444421, 7522222111, 7543331111, 7544443111, 7655554441, 7665555211, 7765554311, 7766654431, 7775222111, 7776444421, 7777543331, 7777776631, 8543333111, 8554443221, 8653332211, 8665433311, 8777552221, 8777655541, 8777755211, 8777766631, 8873333111, 8874444421, 8875333321, 8875444211, 8875543111, 8876422111, 8877543331, 8885443211, 8885444431, 8886222211, 8887776643, 8888773111, 8888866321, 9555544321, 9665555521, 9733333321, 9755222111, 9764442211, 9765554333, 9766553333, 9766655441, 9844441111, 9876554333, 9876666643, 9877541111, 9886544221, 9887773111, 9888765533, 9888766633, 9888775433, 9888777433, 9888832211, 9966555551, 9977663321, 9977777651, 9987666541, 9987731111, 9987766331, 9988664443, 9988865521, 9995555431, 9997554421, 9997753331, 9998443111, 9998654333, 9998754431, 9998865421, 9998873321, 9998885431, 9999643211, 9999765533, 9999888653, 9999974111, 9999985211, 9999997543.