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Euler's Proof on Infinitude of Number of Primes

I've taken this screenshot from this Brilliant Wiki Page.

I don't understand how (2) follows from (1).

Can anyone help me, please, with some details?

8 months, 3 weeks ago

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I agree that this proof is poorly written up. The explanation should go something like this (see page 1 and 2).

@Calvin Lin@Eli Ross you might want to look into this. · 8 months, 3 weeks ago

Thank you very much! · 8 months, 3 weeks ago

Do you follow the proof? If so, can you help us add more explanation into the wiki so that others who are new to it can likewise read and understand? Staff · 8 months, 3 weeks ago