# 37

This number is a prime.

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The smallest isolated prime (i.e., not a member of a twin prime pair) of form 6n + 1. [Beedassy]

The lesser prime of the smallest emirp pair both of which
are Pythagorean, i.e., expressible as the sum of two
squares: 37 = 1^{2} + 6^{2} ; 73 =
3^{2} + 8^{2}. Note that the derived
palindromic prime of the form "primemirp" is also
Pythagorean: 373 = 7^{2} + 18^{2}. [Beedassy]

The smallest emirp separated from its adjacent primes on each side by a prime number of successive composites. [Beedassy]

A prime-digit prime made up of additive persistence
*p* and digital root *r* of
*N ^{N}*, where repdigit

*N*consists of

*d*digits

*d*with

*d*=

*r*-

*p*, i.e., 4 = 7 - 3. [Beedassy]