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The Integral of the Inverse of the Primes
Independent Researcher, Kékkut, Hungary
Independent Researcher, Kékkut, Hungary
- 1 Independent Researcher, Kékkut, Hungary
- 2 Independent Researcher, Kékkut, Hungary
Advances in Pure Mathematics·Volume 13 (2023)·Pages 250–266·Published 11 May 2023·DOI10.4236/apm.2023.135018
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Abstract
The present paper gives the proof of the set of primes as continuum and evaluates the analytical formula for the integral of the inverse of the primes over the distance. First it starts with the density of the primes, shortly recapitulates the prime-number-formula and the complete-prime-number-formula, the proof of the set of primes as continuum. The theoretical evaluation is followed in annexes by numerical evaluation of the theoretical results and of different constants, which represent inherent properties of the set of primes.
KeywordsDensity of PrimesPrime-Number-FormulaComplete-Prime-Number-FormulaGoldbach’s ConjectureTwin PrimesK-Tuples of PrimesPrimes as Continuum
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