Nitpick: It is impossible to pick a positive integer uniformly at random. This is the limit as n goes to infinity of the odds that two uniformly random numbers less than n have no common divisor.
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Good point! Obvious now you say it.
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Humm, exactly Fibonacci ratio of 60,80%.
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Not "them" but "their." Gerund. Opps... have exceeded my weekly pedantry allowance. Fortunately, new one kicks in tomorrow.
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I wish I was better at maths, to get my head around these oddities in a humanly satisfying way. It always feels strange to me when a natural phenomena is explained by a seemingly arbitrary value (6 in this case). Need to work through the proof until I can convince myself.
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I get lost right after "over all primes". How do you get from primes to 1/1-x?
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What goes into this proof are two formulas of Euler : \zeta(s) := \sum_{n =1}^\infty n^{-s} = \prod_{p prime} 1/(1 - p^{-s}) which rephrases unique factorisation of integers in primes, and \zeta(2) = \pi^2/6
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"Divide"?
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I was wondering if this tweet already happened, and indeed it had!
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I want to re-write this in TeX.
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