List all even prime numbers?

Hint: From the question we have been asked to find all the even prime numbers. so, for solving these kinds of basic questions we will take the help of the definition of prime numbers and even numbers. using the definition of prime numbers we will explain what is an even prime number and find all the even prime numbers. so, we proceed with our solution as follows.

Complete step by step answer:
A prime number is one that has its factors only itself and one.
For example,
\[\Rightarrow 1\times 3=3\] and that’s all we can get for three so three is the prime number.
\[\Rightarrow 1\times 4=2\times 2=4\] four has two sets of factors and therefore it is not a prime number.
Generally we can say any number is an even number or not by checking whether it is divisible by \[2\] or not.
If it is divisible by \[2\] then it is an even number in the other case the number will be an odd number.
So, we will interrelate these both definitions and solve our question.
Any even number has \[2\] as a factor so if the number has itself, \[2\] and \[1\] as factors then the given number will not be a prime number.
The number \[2\] is an even number that has only itself and \[1\] as factors.

Therefore, we can say that \[2\] is the only even number that is prime.

Note: Students should have good knowledge in concepts of even numbers and prime numbers in number theory to solve these questions. If the student writes the answer as \[2,3,5,7...\] then our solution will be wrong as except \[2\] remaining numbers are odd numbers.