# 31

This number is a prime.

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31 is the number of the French department of Toulouse where lived Pierre de Fermat, 'Prince of Amateurs' and father of modern number theory. [Beedassy]

31 is the first emirp to appear in the primeth sequence:
P_{1} = 2 ; P_{2} = 3 ;
P_{3} = 5 ; P_{5} = 11 ;
P_{11} = 31. The next emirp 9737333 occurs
after 6 further steps and the third one is not below
10^{25}. [Beedassy]

The only occurrence in the sequence of primes of a pair of
consecutive emirps the next one being "generated" from its
predecessor when expressed in octal scale:
31_{10} = 37_{8}. [Beedassy]

(There are 5 curios for this number that have not yet been approved by an editor.)

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