Euklids proof about the infinitude of primes
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If there were only a finite amount of primes then there would be a largest
prime :latexformula:`p`. However, the number :latexformula:`p! + 1` is not
divisible by any number :latexformula:`1, ..., p`. Therefore, a prime dividing
:latexformula:`p! + 1` has to be bigger than :latexformula:`p`. Therefore there
is an infinite number of primes.