# 59

## Summary

### Factorization

The number 59 is a prime number.

### Properties and families

Property or family Parameter values First few numbers Proof of satisfaction/membership/containment
prime number 17th prime number 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, [SHOW MORE]View list on OEIS divide and check
irregular prime second irregular prime 37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, [SHOW MORE]View list on OEIS
safe prime (prime  such that  is also prime) fifth safe prime 5, 7, 11, 23, 47, 59, 83, 107, 167, [SHOW MORE]View list on OEIS  equals 29 which is prime.
smaller of a pair of twin primes 59 + 2 = 61 which is prime.

## Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 59 for suitable input choice.

Polynomial Degree Some values for which it generates primes Input value  at which it generates 59
 2 all numbers 1-16, because 17 is one of the lucky numbers of Euler. 7