The Riemann hypothesis it has never been solved.is a conjecture about the location of the nontrivial zeros of the Riemann zeta function which states that all non-trivial zeros (as defined below) have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann hypothesis implies results about the distribution of prime numbers that are in some ways as good as possible. Along with suitable generalizations, it is considered by some mathematicians to be the most important unresolved problem in pure mathematics(Bombieri 2000). The Riemann hypothesis is part of Problem 8, along with the Goldbach conjecture, in Hilbert's list of 23 unsolved problems, and is also one of the Clay Mathematics Institute Millennium Prize Problems. Since it was formulated, it has remained unsolved.
The Riemann zeta function ζ(s) is defined for all complex numbers s ≠1. It has zeros at the negative even integers (i.e. at s = −2, −4, −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:The real part of any non-trivial zero of the Riemann zeta function is 1/2.
Thus the non-trivial zeros should lie on the critical line, 1/2 + i t, where t is a real number and i is the imaginary unit.
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The hardest sixth grade math problem is not the same for every student. While some find one area of math to be hard, others consider it to be easy.
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