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graduate texts in harmonic analysis

graduate texts in harmonic analysis

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Graduate Texts in Memes on Facebook
GTM SKINCARE

GTM SKINCARE

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New video by Flammable Maths:
𝗦𝗢𝗡 𝗢𝗙 𝗔 𝗣𝗨𝗧𝗡𝗔𝗠 𝗕𝗢𝗜! Integrating a CRAZY Variant!
https://youtu.be/WFmWCsOT6a0

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Q15
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OmG THiS iS So HArrRD!!!!1!1 VEry HaRd MAth PuZZlE SOLVed!!!111 CaN u Do iT iN HeaD?!?!?!1ß
https://youtu.be/lGwhNKv05Ss

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In number theory, the prime number theorem(PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussinin 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is π(N) ~ N/log(N), where π(N) is the prime-counting function and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N). Consequently, a random integer with at most 2n digits (for large enough n) is about half as likely to be prime as a random integer with at most n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(101000) ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N).

Hoffman, Paul (1998). The Man Who Loved Only Numbers. New York: Hyperion Books, p. 227.

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Graduate Texts in Memes on Facebook
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