31

This number is a prime.

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Moser's circle problem asks to determine the most pieces into which a circle is divided if n points on its circumference are joined by chords with no three internally concurrent. The first few values are 1, 2, 4, 8, and 16. What do you think the next term will be? [Post]

The smallest power of 2 with a pandigital factorization: 536870912 * 4 = 2^31. [Post]

(There are 3 curios for this number that have not yet been approved by an editor.)