31
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This article is about a particular natural number.|View all articles on particular natural numbers
Contents
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 |