# 29

From Number

This article is about a particular natural number.|View all articles on particular natural numbers

## Summary

### Factorization

The number 29 is a prime number.

### Properties and families

Property or family | Parameter values | First few numbers | Proof of satisfaction/membership/containment |
---|---|---|---|

prime number | tenth 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 |
A natural number is prime if and only if is not divisible by any prime less than or equal to . In this case, since is between 5 and 6, verifying primality requires verifying that 29 is not divisible by any prime up to 5, i.e., it is not divisible by 2, 3, or 5. |

Sophie Germain prime (prime such that is prime) | sixth Sophie Germain prime | 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, [SHOW MORE]View list on OEIS |
equals 59, which is prime |

## Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 29 for suitable input choice.

Polynomial | Degree | Some values for which it generates primes | Input value at which it generates 29 |
---|---|---|---|

2 | all numbers 1-16, because 17 is one of the lucky numbers of Euler. | 4 |