The dance between 𝑒 and π continues.. 
The infinite product for 𝑒 becomes the famous Wallis product for π if you replace all the powers with 1pic.twitter.com/CvOWz2KRtz
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Out of curiosity I divided the two equalities, and the Mersenne Number's popped out in the exponent.
A Mersenne Number is of the form 2ⁿ - 1
A Mersenne Number is prime only if 𝑛 is prime
The largest known Mersenne prime is 2⁸²⁵⁸⁹⁹³³-1pic.twitter.com/Hms50narC4
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For those interested, there’s a nice review paper (with other very neat identities) here : https://arxiv.org/pdf/1005.2712.pdf …
This infinite product for e/2 wasn’t discovered until 1980 by Nicholas Pippenger.
The proof only makes use of Stirling’s formula!Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo
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It's almost Ramanujan-istic.
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I feel as if Ramanujan could have done all of this in his head, and then just for shits write it as a continued fraction.
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but 2^1 - 1 isn’t Mersenne
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mersenne numbers, not primes ;)
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I need to show you how Mersenne primes can predict the EM and grav coupling constants. Pure math > physics.
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I need to learn how to post a YouTube clip into a video, there's a way to specify position but I don't know it. I would attach Feynman, in one of the quantum mechanical view of reality lectures saying, "I really do think quantum mechanics is right."
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Is the next exponent 2^4 or 2^5 tho??
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