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Maths question, product of (p/p-1)

What is the Product to infinity of p/p-1, where p is prime.
I'm trying to find it out, due to some curiosity on abundacy of numbers.
Original post by blademan9999
What is the Product to infinity of p/p-1, where p is prime.
I'm trying to find it out, due to some curiosity on abundacy of numbers.


pPpp1=pP111/p=nZ1n \displaystyle \prod_{p \in P} \frac{p}{p-1} = \prod_{p \in P} \frac{1}{1-1/p} = \sum_{n \in Z} \frac{1}{n}

which diverges. This is the substantial step from Euler's proof of the infinitude of primes.

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