The Integral of the Inverse of the Primes  

作　　者：Pal Doroszlai Horacio Keller Pal Doroszlai;Horacio Keller(Independent Researcher, Kékkut, Hungary)

机构地区：[1]Independent Researcher, Kékkut, Hungary

出　　处：《Advances in Pure Mathematics》2023年第5期250-266,共17页理论数学进展（英文）

摘　　要：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.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.

关 键 词：Density of Primes Prime-Number-Formula Complete-Prime-Number-Formula Goldbach’s Conjecture Twin Primes K-Tuples of Primes Primes as Continuum 

分 类 号：O15[理学—数学]