# 31

This number is a prime.

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^{31}- 1)/(31 - 1) is prime. [Capelle]

3^31 - 2^31 is prime. [Capelle]

The largest known prime number such that the digits of its square are in descending order. [Capelle]

The largest known prime number p such that the decimal
expansion of 3^{p} does not
contain any zero. [Capelle]

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