31

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

Summary

Factorization

The number is a prime number.

Properties and families

Property or family Parameter values First few numbers Proof of satisfaction/membership/containment
prime number 11th 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 checking that 31 i not divisible by any prime up to 5, i.e., it is not divisible by 2, 3, or 5.
Mersenne number , i.e., plug and check
Mersenne prime (both a Mersenne number and a prime number)
regular prime 10th regular prime (note that 2 is neither a regular nor an irregular prime) 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, [SHOW MORE]View list on OEIS
Euclid number number that is of the form primorial + 1 2, 3, 7, 31, 211, 2311, View list on OEIS 30 is a primorial: it is the product of the first three primes

Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 31 for suitable input choice.

Polynomial Degree Some values for which it generates primes Input value at which it generates 31
2 all numbers 1-10, because 11 is one of the lucky numbers of Euler. 5
2 all numbers 0-28 1

Multiples

Interesting multiples

Number Prime factorization What's interesting about it
341 11 times 31 smallest Poulet number (also called Sarrus number), i.e., smallest Fermat pseudoprime to base 2
2821 7 times 13 times 31 one of the Carmichael numbers, i.e., absolute pseudoprimes