Extending Rosser's Theorem

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Let be the number of primes up to . The prime number theorem states that and implies that , where is the prime. Rosser proved that for all . Rosser's theorem was extended to , for all .

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The curves plotted are (blue), (khaki), and (brown).

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Contributed by: Jon Perry (April 2011)
Open content licensed under CC BY-NC-SA


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