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In the paper the new formulae for the prime counting function π:
(where σ is the sum-of-divisor function and ψ is the Dedekind’s function) are proposed and proved. Also a general theorem (Theorem 1) is obtained that gives infinitely many explicit formulae for the prime counting function π (depending on arbitrary arithmetic function with strictly positive values, satisfying certain condition).
- Prime number
- Composite number
- Arithmetic function
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Cite this paper
Vassilev-Missana, M. (2013). New explicit representations for the prime counting function. Notes on Number Theory and Discrete Mathematics, 19(3), 24-27.