31

This number is a prime.

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The sum of the reciprocals of the digits of 2^31 equals 22/7 (grade school approximation of π). [Gaydos]

California is the 31st U.S. state and its postal code is CA, the 3rd and 1st letters of the alphabet. [Gaydos]

A repunit of 31 ones is a prime number in base 31. [Gaydos]

The 13353rd century has 31 abundant years. The next such century is the 27339th. Are there any centuries with 32 or more? [Gaydos]

There are 31 prime numbers that have sums of reciprocals of digits that are less than 1/2. [Gaydos]

The number of "cursed composites" that are semiprime. Computing the number of cursed composites with square-free factors is a beastly task. [Gaydos]