29

This number is a prime.

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Bhargava and Hanke proved that if an integer valued quadratic form (such as 3x² + 2xy + 4y²) can represent the numbers 29 numbers: 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203 and 290; then it can represent every positive integer. [Caldwell]

A prime p is the length of the hypotenuse of a Pythagorean triangle if (and only if) p = 4n+1. The first primes for which the area of these right triangle are equal are 29 and 37. (The area is the product of the first four primes.) [Caldwell]