Prime Number

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, and 19. Numbers that are not prime, like 4, 6, 8, and 9, are called composite numbers. Composite numbers can be split into smaller factors. For example, 6 equals 2 times 3, and 9 equals 3 times 3.

The number 2 is the only even prime. Every other even number can be divided by 2, so it cannot be prime. The number 1 is not counted as a prime, even though it can only be divided by itself. Mathematicians made this rule because it makes other math rules work better.

Primes are sometimes called the building blocks of numbers. Every whole number larger than 1 can be made by multiplying primes together in just one way. The number 12 is 2 times 2 times 3. The number 30 is 2 times 3 times 5. This idea is called the fundamental theorem of arithmetic. It is one of the most important rules in all of math.

How many primes are there? The answer is infinite. The Greek mathematician Euclid proved this more than 2,000 years ago. No matter how high you count, you will always find another prime. They do get harder to find, though. As numbers grow bigger, primes spread farther apart. Among the first ten numbers, there are four primes. Among ten numbers near a billion, you might find only one or two.

Primes also have strange patterns that no one fully understands. Twin primes are pairs of primes that differ by 2, like 11 and 13, or 17 and 19. Mathematicians believe there are infinitely many twin primes, but nobody has been able to prove it. This is called the twin prime conjecture, and it is one of the most famous open problems in math.

Primes are not just a puzzle. They keep your information safe online. When you send a message, log into a game, or buy something on a phone, the data is scrambled using huge prime numbers, often hundreds of digits long. To unscramble the message, a computer would need to figure out which primes were used. That is so hard that even the fastest computers cannot do it in any reasonable time. A simple idea from ancient Greece now protects nearly every secret on the internet.