29

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] 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 View list on OEIS	A natural number $n>1$ is prime if and only if $n$ is not divisible by any prime less than or equal to ${\sqrt {n}}$. In this case, since ${\sqrt {29}}$ 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 $p$ such that $2p+1$ is prime)	sixth Sophie Germain prime	2, 3, 5, 11, 23, 29, 41, 53, 83, 89, [SHOW MORE] 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559 View list on OEIS	$2(29)+1$ 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 $n$ at which it generates 29
$n^{2}-n+17$	2	all numbers 1-16, because 17 is one of the lucky numbers of Euler.	4