Prime Number

Prime numbers are natural numbers that are not products of two smaller natural numbers, a composite number is a number greater than 1 but not a prime.

For example, 5 has no way of being expressed as a product other than 5 itself, and 4 is a composite number since it is a product of two smaller natural numbers. Prime numbers are fundamental to number theory as a result of the fundamental theorem of arithmetic.

Prime numbers 1 to 100 are those numbers that are starting with 1 and have only two factors: themselves and 1. A factor can be divided equally into another number. The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Primality is the property that all natural numbers greater than 1 are either prime themselves or can be factored into a product of primes that corresponds to their order. A simple but slow method for testing the primality of a given number n is called trial division. Consequently, 4 is composite since it is the product of two prime numbers greater than 4. Primes are central to number theory since they are the foundation of arithmetic: all positive integers greater than 1 are either primes or products of primes that are unique up to their order.

Composite numbers are those numbers that have more than two factors, but a prime number cannot be a composite number.

## First 100 Prime Numbers

The prime numbers from 1 to 100 are 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.

## Why 1 is Not a Prime Number

One does not qualify as a prime number according to the definition of prime numbers, since a prime number is a natural number greater than one that does not result from the addition of two smaller natural numbers.

## Properties of Prime Numbers 1 to 100

The properties of prime numbers are:-

- There is at least one prime number that can be divided by every positive number greater than one
- For any even positive integer greater than 2, you can express the sum of two prime numbers mathematically.
- The prime factors that make up a composite number are all unique, so all composite numbers can be factored into prime factors.

## How to Find Prime Numbers 1 to 100

You can determine whether or not the given number n is a prime number using either of the following two methods: Method 1: 2 is the only even prime number, and there are only two consecutive natural numbers that are prime, which are 2 and 3. Apart from those two regular prime numbers, any prime number can be written as either 6n + 1 or 6n – 1 (unless it is a multiple of one of the regular prime numbers, i.e. 2, 3, 5, 7, 11,13, 17,19,23), where n is a natural number.

For example:

6(1) – 1 = 5

6(1) + 1 = 7

6(2) – 1 = 11

6(2) + 1 = 13

6(3) – 1 = 17

6(3) + 1 = 19

6(4) – 1 = 23

## How to Calculate Prime Numbers Greater Than 40?

This is the formula to calculate prime numbers** **greater than 40.

n2 + n + 41, where n = 0, 1, 2, ….., 39

For example:

(0)2 + 0 + 41 = 41

(0)2 + 1 + 41 = 43

(0)2 + 2 + 41 = 47

**Example 1:** 53 is a prime number or not?

**Solution:**

The factors of 53 are 1 and 53.

Or

Let the given numbers be written in this form of n2 + n + 51.

(1)2 + 1 + 51 = 2 + 51 = 53

So, 53 is a prime number.

**Example 2: **Find if 64 is a prime number or not?

**Solution:**

The factors of 32 are 1, 2, 4, 8, 16, 32, 64.

It has more factors, other than 1 and 64.

Therefore, it is a composite number and not a prime number.