I am afraid that the proof of this equality requires the Fundamental Theorem of Arithmetic, and for the FTA to hold it is necessary that the primes are infinitely many.
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the proof of FTA doesn't use that there are infinitely many primes. The proof of Euler's formula doesn't seem to use it either. So I don't see anything circular here.
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Square of an irrational number can be rational.
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But pi is transcendental.
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Riemann Hypothesis is still not proven right? Starting the sentence with "Since ... " would imply it's true but no proof.
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ζ(2) = π²/6, that’s all!
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though the infinitude of primes is relatively trivial and the irrationality of pi^2 is very hard.
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What's p? And the symbol before the bracket?

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That's meant to be the uppercase pi, which means product.
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Given the above, what could be the product of two irrational? The mind reels.pic.twitter.com/tz78lfMrrp
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