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pandigital  and  unprimeable n.

First numbers that belong to both sets:

894, 898, 1070, 1138, 1142, 1334, 1346, 1358, 1646, 1670, 1766, 1790, 1922, 2070, 2102, 2402, 2566, 2582, 2586, 2826, 8345, 8630, 8980, 10545, 10570, 10575, 11200, 11220, 11345, 11370, 11560, 11765, 11840, 11870, 12125, 12130, 12770, 13055, 13085, 13505, 14060, 14115, 14130, 14160, 14350, 14355, 14390, 14800, 15000, 15945, 16355, 16375, 16390, 16405, 16535, 16795, 17525, 17645, 17670, 19510, 19615, 19630, 19645, 19830, 20315, 20370, 20490, 20580, 20670, 20795, 20975, 21090, 21425, 21450, 22165, 22410, 22825, 22830, 22915, 22950, 23645, 23650, 23705, 23720, 23935, 23965, 24260, 24275, 24295, 24380, 24385, 24560, 24565, 24725, 24830, 25205, 25505, 25590, 25680, 25720, 25780, 25850, 26075, 26125, 26285, 26795, 26850, 26965, 26970, 27025, 27150, 28565, 28580, 28745, 28760, 28910, 28955, 28985, 29600, 29605, 29890, 29905, 29960, 29965, 30120, 30170, 30280, 30745, 31415, 31425, 31445, 31520, 31595, 31675, 31735, 31805, 31820, 31835, 31940, 31945, 32240, 32275, 32525, 32540, 32595, 32855, 33065, 33125, 33230, 33555, 33835, 34025, 34095, 34110, 34375, 34410, 34525, 34795, 34830, 35045, 35075, 35180, 35185, 35240, 35455, 36110, 36120, 36145, 37675, 37700, 37705, 37820, 37910, 37920, 38025, 38070, 38125, 38130, 38240, 38245, 39260, 39475, 39590, 39680, 39685, 39800, 40300, 40310, 40335, 40720, 40740, 40980, 41060, 41150, 41635, 41820, 41835, 42145, 42265, 42270, 43080, 43140, 43210, 43240, 43345, 43350, 43670, 43680, 43705, 44145, 44300, 44390, 44400, 44550, 44605, 44760, 129135, 130665, 130995, 133935, 152925, 159885, 160125, 162195, 169035, 173115, 174885, 179865, 184095, 191985, 193065, 194385, 197865, 199545, 200415, 207885, 208155, 209895, 210975, 211605, 223515, 227325, 230625, 231735, 231885, 239655, 247215, 247965, 248415, 251595, 265185, 265635, 266745, 268035, 268425, 287985, 299835, 306285, 306795, 310035, 314835, 317115, 318015, 318045, 321975, 323295, 328605, 331005, 337935, 340095, 346125, 346785, 347025, 360015, 363225, 368985, 371265, 371685, 372075, 376215.

Some larger examples :