31

This number is a prime.

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© Baskin-Robbins

If t(n) represents the nth triangular number, then 31 is the smallest prime of the form t(p) + t(q), where p and q are themselves prime. [Rupinski]

The smallest prime that is a generalized repunit in three different bases. [Rupinski]

The largest integer such that the average number of triangular numbers required to express the integers less than or equal to it is exactly two. [Rupinski]