# 19

From Number

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## Contents

## Summary

### Factorization

The number 19 is a prime number.

## Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 19 for suitable input choice.

Polynomial | Degree | Some values for which it generates primes | Input value at which it generates 19 |
---|---|---|---|

2 | all numbers 1-16, because 17 is one of the lucky numbers of Euler. | 2 |

## Multiples

### Interesting multiples

Number | Prime factorization | What's interesting about it |
---|---|---|

1729 | 7 times 13 times 19 |
third Carmichael number, i.e., absolute pseudoprime Smallest number expressible as a sum of two positive cubes in two different ways. |