If a number cannot be divisible evenly by anything except itself and 1, then it is known as a prime number. For example, 17 is a prime number, because the only factors of 17 are 1 and 7. So, only 1and 17 can divide 17. Thus a prime number is a whole number which is greater than one and has exactly two factors, 1 and itself. Some prime numbers are 3,5,7,9 etc. We will learn the prime number formula with examples in this article. Let us learn it!

**What is a Prime Number?**

Prime numbers are unique in nature. These are divisible by only 1 and itself. On the other hand, a composite number is a whole number that is greater than one and has more than two factors. Also, the number 1 is neither prime nor composite.

To prove whether a number is a prime number, we need to try for dividing it by 2, and see if we get a whole number. If we do, it can’t be a prime number. If we don’t get a whole number, then next try dividing it by prime numbers: 3, 5, 7, 11 and so on.

**Formula for Prime Number**

How do we determine to know if a number is prime or not? Let us take a look at prime number formula to find the answer.

To calculate it one has to need to find the factors of the number. Take for example 13, 13 is divisible only by 1 and itself. Since it has only two factors, then it is a prime number.

### Interesting Facts about Prime Numbers

- The only even prime number is much obvious number 2. All other even numbers are even.
- If the sum of a number’s digits is a multiple of 3 then that number will be divisible by 3.
- No prime number greater than 5 will be ending with 5. Any number greater than 5 which ends at 5, then will be divisible by 5.
- Zero and 1 are not considered as the prime numbers.
- Except for 0 and 1, a number is either will be a prime number or a composite number.

**Some Applications**

Prime numbers are having many applications in science. It is a fact that we can represent all prime numbers, except 2 and 3, in the form 6n+-1). Prime numbers are at the heart of Cryptography and data security and encryption. And generating things such as finite fields. Important applications of prime numbers are their role in producing error-correcting codes using finite fields.

These are useful in telecommunication to ensure that the messages can be sent and received with automatic correction. Also, their role in ciphers such as RSA is very much popular. It is very difficult to enumerate every application as there are simply infinitely many of them.

**Solved Examples for Prime Number Formula**

Question 1: Find if 73 is a prime number or not?

Solution: The factors of 73 are 1 and 73.

So 73 is only divisible by 1 and 73.

So, 73 is a prime number.

Question 2: Check if 34 is a prime number or not?

Solution: The factors of 1, 2, 17 and 34.

Hence 34 is a composite number and not a prime number.