What is the next prime number after 31?

The next prime number after 31 is indeed 37, as prime numbers are defined as numbers greater than 1 that have no positive divisors other than 1 and themselves.

To determine whether a number is prime, you can test for divisibility by any prime number up to the square root of that number. For 37, the only prime number you would need to check for divisibility is 2, 3, and 5, none of which evenly divide 37.

In contrast, 33 and 39 are not prime because they can be divided evenly by other numbers: 33 can be divided by 3 and 11, while 39 can be divided by 3 and 13. Therefore, they are composite numbers.

The number 37, standing alone in its primality, confirms itself as a prime number, and thus it is the correct answer as the next prime number after 31.