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If there is a limited set of primes, then you can get all the primes and multiply them together. However, if you add one to the number, it will not have any prime factors because all the prime factors have been in the previous number and if you add one to a number, all the prime factors in the previous number do not go into it. Thus, the new number is a prime. |
If there is a limited set of primes, then you can get all the primes and multiply them together. However, if you add one to the number, it will not have any prime factors because all the prime factors have been in the previous number and if you add one to a number, all the prime factors in the previous number do not go into it. Thus, the new number is a prime. |
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[[Category:Number of primes]] |
[[Category:Number of primes]] |
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[[Category:Important Pages]] |
[[Category:Important Pages]] |
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Revision as of 06:57, 25 January 2017
Euclid's proof proved that there was an everlasting set of prime numbers. He was the first person to prove this, even though many other mathematicians proved it another way. It is a proof by contradiction- it states the opposite and shows that it is not possible.
The Proof
The proof states the following:
If there is a limited set of primes, then you can get all the primes and multiply them together. However, if you add one to the number, it will not have any prime factors because all the prime factors have been in the previous number and if you add one to a number, all the prime factors in the previous number do not go into it. Thus, the new number is a prime.