# What is a Prime Number?

A prime number is the positive integers having only two factors, 1 and the integer itself. For example, factors of 6 are 1,2,3, and 6, which are four factors in total. But factors of 7 are only 1 and 7, totally two. Hence, 7 is a prime number but 6 is not, instead it is a composite number. But always remember that 1 is neither prime nor composite.

They are numbers, which are only divisible by 1 or the number itself. Another way of defining it is a positive number or integer, which is not a product of any other two positive integers. There is no defined formula to find if a number is prime or not, apart from finding its factors.

First Ten Prime Numbers

The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Note: It should be noted that 1 is a non-prime number.

History of Prime Numbers

The prime number was discovered by Eratosthenes (275-194 B.C., Greece). He took the example of a sieve to filter out the prime numbers from a list of natural numbers and draining out the composite numbers.

Students can practice this method, by writing the positive integers from 1 to 100 and circling the prime numbers, and putting a cross mark to composite numbers.

• Smallest Prime Number: The smallest prime number defined by modern mathematicians is 2. To be prime, a number must be divisible only by 1 and the number itself which is fulfilled by the number 2.
• Largest Prime Number: As of January 2020, the largest known prime number is 2^(82,589,933) – 1 a number that has 24,862,048 digits. It was found by the Great Internet Mersenne Prime Search (GIMPS) in 2018.

#### List of Prime Numbers 1 to 100

As we know, the prime numbers are the numbers that have only two factors which are 1 and the number itself. There are several primes in the number system. Let us provide here the list of prime numbers that are present between 1 and 100, along with their factors and prime factorization.

 Prime Numbers between 1 and 100 Factors Prime Factorisation 2 1, 2 1 x 2 3 1, 3 1 x 3 5 1,5 1 x 5 7 1,7 1 x 7 11 1,11 1 x 11 13 1, 13 1 x 13 17 1, 17 1 x 17 19 1, 19 1 x 19 23 1, 23 1 x 23 29 1, 29 1 x 29 31 1, 31 1 x 31 37 1, 37 1 x 37 41 1, 41 1 x 37 43 1, 43 1 x 43 47 1, 47 1 x 47 53 1, 53 1 x 53 59 1, 59 1 x 59 61 1, 61 1 x 61 67 1, 67 1 x 67 71 1, 71 1 x 71 73 1, 73 1 x 73 79 1, 79 1 x 79 83 1, 83 1 x 83 89 1, 89 1 x 89 97 1, 97 1 x 97

#### Prime Numbers 1 to 200

Here is the list of prime numbers from 1 to 200, which we can learn and also crosscheck if there exist any other factors for them.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.