The Riemann Hypothesis

$1 Million Millennium Problem #1

The Riemann Hypothesis

What, if any, is the pattern of the prime numbers among all counting numbers?

Mathematicians agree that finding possible solutions to the Riemann Hypothesis (1859) would most likely answer this question.  Euclid proved there is no largest prime number (ca. 350 BC).

But establishing a pattern for finding prime numbers other than noting they occur less frequently as numbers grow larger has eluded investigators. Most knowledgeable mathematicians agree that a solution of the Riemann Hypothesis would add to our understanding of how prime numbers are distributed.

See Keith Devlin's "The Millennium Problems: The Seven Greatest Unsolved Puzzles of Our Time, Basic Books, 2002.
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