## Most recent change of PrimeNumber

Edit made on June 09, 2013 by ColinWright at 14:19:54

Deleted text in red / Inserted text in green

WW WM
A PrimeNumber Prime Number is a positive whole number that is divisible
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 /p/ EQN:p such that if /p/ EQN:p divides a product /ab,/ EQN:ab, then /p/ EQN:p divides /a,/ EQN:a, or /p/ EQN:p divides /b,/ EQN:b, or both.
or
* A !/ prime !/ is a positive number /p/ EQN:p such that it has exactly two positive divisors, itself and 1.

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. For one One proof that there are infinite primes see of this (there is more than one)

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