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It is impossible to list all the prime numbers as there are an infinite number of them.

The list of prime numbers starts: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

Suppose you could list all the prime numbers and have done so - there is no Prime number which is not on the list.

Multiply them all together and add 1.

This number is not divisible by any of the listed prime numbers as there is always a remainder of 1. So either this new number is a prime number, or there is another prime number not listed which will divide into it.

Which means that the list was not all the prime numbers; meaning it is impossible to list all the prime numbers.

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12y ago

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Q: What are all the pime numbers?
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