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A

only by itself and 1. (and their negatives (of course)).

[[[>50 You have to be a bit careful here. The usual

definitions are a bit loose. There are two definitions

that are much tighter.

* A !/ prime !/ is a positive number

or

* A !/ prime !/ is a positive number

The first of these would mean that 1 is a prime. The second would mean that 1 is /not/ a prime.

On every other positive number they agree, and that's why the question of whether or not 1 is

a prime is regarded as a matter of convention, or ignored altogether.

]]]

For example 2, 3, 5, 7, 11, ...

Euclid in around 300BC proved that there are infinitely

many primes.

is on the page about Proof By Contradiction.

There are still many things unknown about primes.

For example, look at Prime Pairs or Goldbach's Conjecture.

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One way of thinking about primes is like this ...

* Suppose you have 35 marbles. You can arrange them in a row, but you can also arrange them in a rectangle, 7 by 5.

* Suppose you have 28 marbles. You can arrange them in a rectangle, 7 by 4, or 14 by 2.

* Suppose now you have 29 marbles. You can't arrange them in a (non-trivial) rectangle, no matter how hard you try. That's because you can't find two positive whole numbers bigger than 1 that multiply to give 29.

** 29 is prime.

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One of the uses of prime numbers is in cryptography, especially the RSA Cryptosystem.

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CategoryMaths