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polymathprojects.org | ||
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terrytao.wordpress.com
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| | | | | Building on the interest expressed in the comments to this previous post, I am now formally proposing to initiate a Polymath project on the topic of obtaining new upper bounds on the | |
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thatsmaths.com
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| | | | | The Riemann Hypothesis Perhaps the greatest unsolved problem in mathematics is to explain the distribution of the prime numbers. The overall ``thinning out'' of the primes less than some number $latex {N}&fg=000000$, as $latex {N}&fg=000000$ increases, is well understood, and is demonstrated by the Prime Number Theorem (PNT). In its simplest form, PNT states that... | |
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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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thisandthatthenextpart.wordpress.com
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