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Fundamental theorem of arithmetic

The fundamental theorem of arithmetic states:

Every integer greater than 1 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not.

 


Examples

On a Casio fx-82EX calculator, you can see that

666 = 2 × 32 × 37
1014 = 2 × 3 × 132
6936 = 23 × 3 × 172

 


History

The theorem was described by the Greek mathematician Euclid, but the first complete proof appeared in 1801 in the Disquisitiones Arithmeticae by the German mathematician Carl Friedrich Gauß.


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