61

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

Summary

Factorization

The number 61 is a prime number.

Properties and families

Property or family Parameter values First few numbers Proof of satisfaction/membership/containment
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 divide and check
regular prime 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, [SHOW MORE]View list on OEIS

Waring representations

Sums of squares

Template:Square sums facts to check against

Item Value
unique (up to plus/minus and ordering) representation as sum of two squares . Note that existence and uniqueness both follow from it being a prime that is 1 mod 4.
This also corresponds to the factorization in the ring of Gaussian integers .
representations as sum of three squares (up to ordering and plus/minus equivalence)

Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 61 for suitable input choice.

Polynomial Degree Some values for which it generates primes Input value at which it generates 61
2 all numbers 1-40, because 41 is one of the lucky numbers of Euler. 5
2 all numbers 0-28 4