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How many prime numbers exist? - Answers

There are an infinite amount of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof: # Suppose there are n prime numbers overall. # Let N be a common multiple of all these primes. # Is N+1 prime? If it is, we have found a new prime. # Suppose N+1 is not prime. Thus, there exists a Prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.



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How many prime numbers exist? - Answers

https://math.answers.com/basic-math/How_many_prime_numbers_exist

There are an infinite amount of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof: # Suppose there are n prime numbers overall. # Let N be a common multiple of all these primes. # Is N+1 prime? If it is, we have found a new prime. # Suppose N+1 is not prime. Thus, there exists a Prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.



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https://math.answers.com/basic-math/How_many_prime_numbers_exist

How many prime numbers exist? - Answers

There are an infinite amount of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof: # Suppose there are n prime numbers overall. # Let N be a common multiple of all these primes. # Is N+1 prime? If it is, we have found a new prime. # Suppose N+1 is not prime. Thus, there exists a Prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.

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      There are an infinite amount of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof: # Suppose there are n prime numbers overall. # Let N be a common multiple of all these primes. # Is N+1 prime? If it is, we have found a new prime. # Suppose N+1 is not prime. Thus, there exists a Prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.

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