Does the Riemann Hypothesis Follow from the Prime Number Theorem?

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SUMMARY

The discussion asserts that the Riemann Hypothesis is a consequence of the Prime Number Theorem (PNT). It highlights that as n increases, the density of prime numbers decreases, and the term n^1/2 diminishes the influence of larger n on the results. The conclusion drawn is that the Riemann Hypothesis logically follows from the implications of the Prime Number Theorem, although some participants express confusion regarding this relationship.

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  • Understanding of the Prime Number Theorem (PNT)
  • Familiarity with the Riemann Hypothesis
  • Basic knowledge of number theory
  • Concepts of prime number distribution
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mustang19
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There are fewer primes for larger n. The n^1/2 just makes the larger n have less impact on the result. So the riemann hypothesis follows from pnt. Does this make any sense to you?
 
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Nope.
 
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