How Many Even Prime Numbers are There

Introduction

There is only one even prime number. Before we arrive at the answer to this question first we have to go through what the prime number and the even number mean. As such, it is clear that we have to identify those unique numbers that have both the properties of a prime number and an even number. We will also explore if there are some terms opposite in meaning with respect to the prime numbers and the even numbers. In mathematics, we come across various properties of numbers and accordingly we segregate them into various groups. Isn’t it right? Let us know more about these concepts in detail.

What is a Prime Number?

To check if a number is a prime one or not, we have to factorize the number. When after performing the factorization of the number we get that the number reflects only two factors (the number itself, and 1), we confirm that it is a prime number. Examples of prime numbers are 2, 3, 5, 7, etc.

What is The Antonym of Prime Numbers?

Basically, the term that we employ to denote the numbers opposite in meaning to the prime numbers is composite numbers.

Note that when any number is factorized and it releases more than two factors of the number, we get a composite number.

Examples of composite numbers are 4,6,9, etc.

What is an Even Number?

To check if a number is an even one or not, we have to divide the number by 2. When the number 2 completely divides any number keeping no remainder behind, we get an “even number”,

Examples of even numbers are 2, 4, 6, 8, etc.

What is The Antonym of Even Numbers?

Fundamentally, the term that we hire to represent the numbers opposite in meaning to the even numbers is the odd numbers.

Thus, the number that is not completely divisible by 2, but generates a remainder behind, is an “odd number”.

Examples of odd numbers are 3, 5, 7, 9, etc.

How Many Even Prime Numbers are There?

To check if a number is even and at the same time a prime number, we write down the list of even numbers and the list of the prime numbers separately. Then we will mark the common ones which will provide us with the required answer.

The even numbers are 2, 4, 6, 8, 10, 12, and so on.

The prime numbers are 2, 3, 5, 7, 11, 13, and so on.

From the above data, it is clear that the only number that is common to both the groups of even and prime numbers is the number 2 only.

Hence, in this vast number system with infinite numbers, we find only one even prime number.

Conclusion

• There is no overlap between the prime numbers and the composite numbers.

• There is no overlap between the even numbers and the odd numbers.

• We have one number that neither belongs to the set of prime numbers nor is included in the set of composite numbers. This unique number is one.

• Every positive integer falls under the category of either an even number or an odd number.

• The frequency of occurrence of even numbers alternates with the frequency of odd numbers in the number line.

• The frequency of occurrence of prime numbers does not alternate with the frequency of composite numbers in the number line. Both are irregular.

Hence, there is only one even prime number which is “2”