# Prime Numbers and Composite Numbers

## Prime Numbers

Prime numbers are integers greater than 1 that can only be divided by themselves and 1. For example, 5 is a prime number because it has only two factors: 1 and 5. It is not divisible by 2, 3, or 4.

Another example is the number 7, which is also a prime number because it can only be divided by 1 and 7.

The number 2 is the first prime number and is unique because it is the only even prime number. After 2, all prime numbers are odd.

The first few prime numbers are:

Note that 1 is not considered a prime number since it only has one distinct factor.

### Unsolved Problems in Prime Numbers

There are many unsolved problems related to prime numbers. One famous example is the Goldbach Conjecture, which states that every even number greater than or equal to 4 can be represented as the sum of two prime numbers.

• We do not know whether there is a finite number of twin primes or an infinite number of them.

Another unsolved problem is the Twin Prime Conjecture, which states that there are an infinite number of prime pairs that differ by 2, such as , and so on.

## Composite Numbers

Numbers that are not prime are considered composite numbers. The number 1 is neither prime nor composite. The first composite number is 4, followed by and so on.

Composite numbers have more than two factors. Every composite number can be expressed as a unique product of prime factors. For example:

This unique representation of composite numbers as a product of prime factors is known as the Fundamental Theorem of Arithmetic. Prime numbers can be thought of as the building blocks of composite numbers.

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