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Pierpont prime  and  twin primes

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(max 15 digits)

First numbers that belong to both sets:

3, 5, 7, 13, 17, 19, 73, 109, 193, 433, 1153, 2593, 65537, 139969, 472393, 786433, 995329, 57395629, 63700993, 169869313.