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Can quantum computing solve the Riemann hypothesis?
A new quantum algorithm allows the computation of a range of prime number functions to be computed well beyond the limits of a conventional computer. It is even possible that it could solve the million-dollar Riemann hypothesis.
What is the significance of Riemann hypothesis?
Considered by many to be the most important unsolved problem in mathematics, the Riemann hypothesis makes precise predictions about the distribution of prime numbers. As the name suggests, it is for now only a conjecture.
Is the Riemann hypothesis proven?
Most mathematicians believe that the Riemann hypothesis is indeed true. Calculations so far have not yielded any misbehaving zeros that do not lie in the critical line. However, there are infinitely many of these zeros to check, and so a computer calculation will not verify all that much.
Is it possible to convert the Riemann hypothesis into a quantum equation?
Mathematicians have long suspected that there might be a way to convert the Riemann hypothesis into an equation similar to those used in quantum physics. The zeros of the zeta function could then be calculated the same way physicists calculate the possible energy levels for an electron in an atom, for example.
What would happen if the Riemann hypothesis failed?
Conversely, as the number theorist Enrico Bombieri wrote in his description of the problem, “the failure of the Riemann hypothesis would create havoc in the distribution of prime numbers.” As mathematicians have attacked the hypothesis from every angle, the problem has also migrated to physics.
How did Riemann prove that all zeros have real parts?
Riemann calculated the first few nontrivial zeros of the zeta function and confirmed that their real parts were equal to ½. The calculation supported his hypothesis that all zeros had this property, and thus that the spacing of all prime numbers followed from his function.
How did Riemann prove his zeta function was valid?
However, Riemann knew that his formula would be valid only if the zeros of the zeta function satisfied a certain property: Their real parts all had to equal ½. Otherwise the formula made no sense. Riemann calculated the first few nontrivial zeros of the zeta function and confirmed that their real parts were equal to ½.