Efficient Prime Counting and the Chebyshev Primes

  title={Efficient Prime Counting and the Chebyshev Primes},
  author={Michel Planat and Patrick Sol'e},
  journal={arXiv: Number Theory},
The function where is the logarithm integral and the number of primes up to is well known to be positive up to the (very large) Skewes' number. Likewise, according to Robin's work, the functions and , where and are Chebyshev summatory functions, are positive if and only if Riemann hypothesis (RH) holds. One introduces the jump function at primes and one investigates , , and . In particular, , and for . Besides, for any odd , an infinite set of the so-called Chebyshev primes. In the context of… Expand

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