37

Number
$37$ (thirty-seven) is:


 * The $12$th prime number, after $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31$


 * The $4$th centered hexagonal number after $1$, $7$, $19$:
 * $37 = 1 + 6 + 12 + 18 = 4^3 - 3^3$


 * The $11$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $\ldots$


 * The $4$th emirp after $13$, $17$, $31$


 * The $9$th permutable prime after $2, 3, 5, 7, 11, 13, 17, 31$.


 * The $2$nd integer which has a reciprocal whose period is $3$:
 * $\dfrac 1 {37} = 0 \cdotp \dot 02 \dot 7$


 * The $5$th of $5$ primes of the form $2 x^2 + 5$:
 * $2 \times 4^2 + 5 = 37$


 * The $3$rd of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 2^2 + 29 = 37$


 * The $27$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{37} = 137 \, 438 \, 953 \, 472$


 * The $23$rd positive integer after $2, 3, 4, 7, 8, \ldots, 26, 29, 30, 31, 32, 33$ which cannot be expressed as the sum of distinct pentagonal numbers.


 * The $4$th prime number of the form $n^2 + 1$ after $2, 5, 17$:
 * $37 = 6^2 + 1$


 * Every positive integer can be expressed as the sum of at most $37$ positive $5$th powers.

Also see

 * Period of Reciprocal of 37 has Length 3
 * Numbers whose Cyclic Permutations of 3-Digit Multiples are Multiples
 * Hilbert-Waring Theorem for $5$th Powers