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Poulet n.  and  Proth n.

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(max 15 digits)

First numbers that belong to both sets:

1729, 4033, 8321, 12801, 65281, 130561, 348161, 3225601, 8355841, 8384513, 16773121, 40280065, 104988673, 2147418113, 4294901761, 4294967297, 53282340865, 68719214593, 137439477761.