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Let Nk denote the kth primorial and let K(x) be the primorial counting function, the function that counts the number of primorials not exceeding x. In this note, we examine the sign of the functions K(x)−π( log x) and K(x)−li( log x) and find a new necessary and sufficient criterion for the truth of the Riemann hypothesis.
Christian Axler (Wed,) studied this question.
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