Mathematics

An Introduction to Prime Numbers



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Prime numbers are the fundamental building blocks of mathematics. Just like the atoms that make up the world around us, prime numbers are the most basic units of the mathematical world and cannot be split any further.

Most numbers can be broken down and expressed as a multiplication of one or more other numbers. Take the number 12, for instance. This can be expressed as 1 multiplied by 12, or 3 multiplied by 4, or 6 multiplied by 2. There are some numbers, however, that cannot be split in this way. Take the next number along, number 13. Can you think of any numbers that divide neatly into that? Only the numbers 1 and 13 can be divided into 13 without any remainders. This means that 13 is a prime number, a number that is only divisible by 1 and itself.

So prime numbers can't be divided themselves, but they can be multiplied together to make every other number. Going back to our example of the number 12, we can create this by multiplying the prime numbers 2 and 3, since 12 can be expressed as 2 multiplied by 2 multiplied by 3. If you look at any number greater than 1, you'll be able to create it by multiplying two or more prime numbers together. This is called the prime number decomposition theory'.

Let's look at all the prime numbers less than 100: 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. You'll see there is no obvious pattern that can be used to generate a list of prime numbers. Mathematicians, however, spend a lot of time searching for new primes.

The largest known prime number (as of September 2006) is the 44th Mersenne prime. I would include the actual number in this article but it is 9,808,358 digits long. Imagine typing an article of 15,000 words and you'll have an idea of how many pages it would take to print this number out. That's a truly large number but it's probably not the largest prime. Given that the Greek mathematician Euclid proved that the number of primes is infinite, there will be a larger number that could be prime, it just hasn't been identified yet.

Prime numbers have also given number theorists a range of other mathematical challenges that remain unsolved. One of the most famous is the Goldbach conjecture, that suggests that every even number greater than 2 can be created by adding two prime numbers together.

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