The Case
An interesting result can be found for ΞΆ(1)
which can also be written as,
which is,
as,
thus,
We know that the left-hand side of the equation diverges to infinity, therefore the numerator on the right-hand side (the primorial) must also be infinite for divergence. This proves that there are infinitely many prime numbers.
Read more about this topic: Proof Of The Euler Product Formula For The Riemann Zeta Function
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