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The Prime Number Theorem (or the PNT) is a theorem that concerns the distribution of primes and, subsequently, the gaps between primes. Its first proof date is not known.

Statement of TheoremEdit

The theorem, formally stated, says that:

\lim_{x\to\infty}\frac{\pi(x)}{x/\ln(x)}=1

where \pi(x) is the number of primes up to and including x. This means that for a number x, the number of primes up to and including x approaches x divided by the the log to base e (or the natural log) of x and {x/\ln(x)} becomes a better approximation of \pi(x) as x grows larger. This also means that:

P_x \approx x\ln(x), where P_x is the xth prime number.

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