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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

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Formula for $\pi$ involving exponents of Mersenne primes

Can someone provide a proof for the following claim? $$\pi=\dfrac{S_0S_2}{M_3M_5} \cdot\left(\displaystyle\prod_{p \equiv 1 \pmod{4} } \frac{p}{p-1}\right) \cdot \left(\displaystyle\prod_{p \equiv 3 …
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