Friday, March 17, 2017

A signature of chaos................................the infinite inside the finite........sensitivity to initial conditions..............................and being erratic inside of something not so erratic.....amongst other things...


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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.

Prime number theorem - Wikipedia

https://en.wikipedia.org/wiki/Prime_number_theorem
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Prime number theorem - Wikipedia

https://en.wikipedia.org/wiki/Prime_number_theorem
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.
‎Statement · ‎History of the asymptotic law ... · ‎Proof methodology · ‎Proof sketch
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Prime Number Theorem -- from Wolfram MathWorld

mathworld.wolfram.com › ... › Prime Numbers › Prime Number Theorem
by EW Weisstein - ‎2003 - ‎Cited by 10 - ‎Related articles
Hadamard and de la Vallée Poussin independently proved the prime number theorem in 1896 by showing that the Riemann zeta function has no zeros of the form , in the sense that no deeper properties of are required for the proof (Smith 1994, p. 128; Hardy 1999, pp. 58-60).

The prime number theorem (video) | Khan Academy

https://www.khanacademy.org/...number.../prime-number-theore...
How can we estimate the number of primes up to x?

How many primes are there? - The Prime Pages

https://primes.utm.edu/howmany.html
The prime number theorem tells us the number of primes less than n is about 1/log(n). This pages includes history, theorems, related results and open questions.
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