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Published on June 16th, 2014 | by Liam


Is one a prime number?

Maths has been created and used by humans for a long time. It’s older than English, and much older than Science. Long before the Maths+StatsEnglish language came to be, mathematicians were discussing numbers and studying shapes. And although the ideas of maths have survived through thousands of years, the symbols, numerals and even the language we use have changed.

Over 2000 years ago Euclid wrote one of the first maths textbooks. Euclid’s Elements covered arithmetic and geometry, but it isn’t like a modern day textbook. There were no pictures of shapes. Euclid described all the shapes using words. Even stranger, there were no numbers and there were no equations. All his maths was written out in sentences in Ancient Greek.

It took a long time for things to change. The numerals we use today (1, 2, etc) were invented in India hundreds of years after Euclid, and common symbols such as the plus and equals signs took another 1000 years to appear.

Throughout history there have been many ways of writing ‘7’, but only one idea of seven. There have been many ways of writing addition, but one plus one has always been two. However, some mathematical ideas have changed meaning over the years. And recently, two American mathematicians decided to chart the history of a particularly tricky mathematical question: is one a prime number?

Prime numbers are like the atoms of maths. They can’t be made by multiplying two smaller numbers together. They can only be divided by two numbers – themselves and one. Around 300 years ago, a lot of mathematicians considered one to be a prime number. After all, there are no numbers that divide it except one and itself (also one). But not all mathematicians agreed with this definition.

In 1801, Carl Friedrich Gauss noticed that every whole number can be made by multiplying prime numbers together. With some work, he showed that for each whole number, there was only one prime factorisation that worked. There is only one way to make the number 30 by multiplying primes – you need 2, 3 and 5 (30 = 2 x 3 x 5). But Carl’s amazing idea only works if you think that one is not a prime number.

It took a long time for mathematicians to agree with Carl. But for the last 100 years, most mathematicians have agreed. The number one is not a prime.

So what did Euclid think, 2000 years ago? Euclid thought the smallest prime number was two, but for completely different reasons. In his Elements, Euclid defines a number as being made up of a multitude of ones. Euclid didn’t consider one to be a number, so it couldn’t be a prime number!

More information
On primes and Pluto
The smallest prime research paper (more advanced and pdf)


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