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de Polignac n.  and  hyperperfect n.

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(max 15 digits)

First numbers that belong to both sets:

1232053, 1570153, 1618597, 2708413, 4013833, 7478041, 12064333, 20103001, 20419093, 26249473, 28600321, 35494981, 38749153, 40374013, 46596457, 47842237, 55262737, 61442077, 61599553.