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Duffinian n.  and  primeval n.

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First numbers that belong to both sets:

1037, 1079, 1379, 10123, 10237, 10279, 10367, 10379, 101237, 102347, 102379, 103679, 1002379, 1012349, 1023457, 1023479, 1234579, 1234679.