Courtesy of University of Utahpic.twitter.com/FGjCt8NDJZ
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That is beautiful
Anyone have a link to Euclid's proof handy?
Let pn be the last prime, let P=p1*p2*...pn+1. P is a relative prime to every p, therefore pn is not the last prime.
That's nice but prooving that apery's constant is irrationnal is very hard
Why ζ(3) irrational prove that there are infinitely many primes
Each term is a rational: (p^3)/[(p^3-1)]. If there were only finite terms, the product would also be rational.
if only Euler knew that
Saidak's proof: ∀n>1,∈ℕ has at least one prime factor; n & n+1 are coprime ∴ n×(n+1) has more different prime factors. Continue indefinitely
Awesome.
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