Question

What is the $15^{th}$ prime number, if they are listed in order?

Answer 1

Hint: We are required to know the concept of prime numbers in order to solve such questions. Prime numbers are numbers that are only divisible by 1 and itself. This also means that the only two factors of the prime numbers are 1 and itself. Here, we list all the prime numbers from 2, since it is the smallest prime number, up to the $15^{th}$ prime number. The last prime number of the resulting series gives us the answer to the given question.

Complete step by step solution:
To solve this question, we first need to define what a prime number is with an example. We then list down the 15 prime numbers. A prime number is defined as the number which is divisible by only 1 and itself. For example, 5 is a prime number since it is divisible by 1 and 5 only. In other words, prime numbers can be defined as those numbers whose only factors are 1 and the number itself. In the same example, 5 has factors 1 and 5 only. Therefore, 5 is a prime number.
A composite number is the opposite of a prime number in the sense that is divisible by 2 or more numbers. Or in other words, they are numbers that have factors apart from 1 and the number itself. For example, 6 is a composite number and not a prime number since its factors are 1, 2, 3 and 6.
Now let us list down all the prime factors starting from 2 which is the smallest and the only even prime number:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47…
Hence, as we can see, the prime numbers continue and extend a long way. In this list, the $15^{th}$ prime number is 47. This is a prime number since it is divisible only by 1 and itself. Also, this list is taken in increasing order or the prime numbers starting from 2.

Hence, 47 is the $15^{th}$ prime number, if they are listed in order.

Note: It is important to note that 1 is neither a prime number nor a composite number. This is because the one and only one factor for 1 is 1 itself. It does not contain 2 factors exactly like the prime numbers nor does it contain more than 2 factors like the composite number. 1 is in general referred to as a unique number.