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thatsmaths.com | ||
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www.jeremykun.com
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| | | | | Problem: Prove there are infinitely many primes Solution: Denote by $ \pi(n)$ the number of primes less than or equal to $ n$. We will give a lower bound on $ \pi(n)$ which increases without bound as $ n \to \infty$. Note that every number $ n$ can be factored as the product of a square free number $ r$ (a number which no square divides) and a square $ s^2$. | |
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polymathprojects.org
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| | | | | (From a post "the music of the primes" byMarcus du Sautoy.) A new polymath proposal over Terry Tao's blog who wrote: "Building on the interest expressed in the comments tothis previous post, I am now formally proposing to initiate a "Polymath project" on the topic of obtaining new upper bounds on thede Bruijn-Newman constant.... | |
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xorshammer.com
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| | | | | Mathematical logic has a categorization of sentences in terms of increasing complexity called the Arithmetic Hierarchy. This hierarchy defines sets of sentences $latex \Pi_i$ and $latex \Sigma_i$ for all nonnegative integers $latex i$. The definition is as follows: $latex \Pi_0$ and $latex \Sigma_0$ are both equal to the set of sentences $latex P$ such that... | |
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gilkanelostlayouts.wordpress.com
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