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New Proof That the Sum of the Reciprocals of Primes Diverges

Department of Applied Mathematics to Information Technology and Communications (Telecommunication Engineering), Polytechnical University of Madrid, Avenida Complutense 30, 28040 Madrid, Spain
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Mathematics 2020, 8(9), 1414; https://doi.org/10.3390/math8091414
Received: 12 July 2020 / Revised: 17 August 2020 / Accepted: 20 August 2020 / Published: 24 August 2020
In this paper, we give a new proof of the divergence of the sum of the reciprocals of primes using the number of distinct prime divisors of positive integer n, and the placement of lattice points on a hyperbola given by n=pr with prime number p. We also offer both a new expression of the average sum of the number of distinct prime divisors, and a new proof of its divergence, which is very intriguing by its elementary approach. View Full-Text
Keywords: number theory; primes; reciprocals of primes number theory; primes; reciprocals of primes
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MDPI and ACS Style

Jara-Vera, V.; Sánchez-Ávila, C. New Proof That the Sum of the Reciprocals of Primes Diverges. Mathematics 2020, 8, 1414. https://doi.org/10.3390/math8091414

AMA Style

Jara-Vera V, Sánchez-Ávila C. New Proof That the Sum of the Reciprocals of Primes Diverges. Mathematics. 2020; 8(9):1414. https://doi.org/10.3390/math8091414

Chicago/Turabian Style

Jara-Vera, Vicente, and Carmen Sánchez-Ávila. 2020. "New Proof That the Sum of the Reciprocals of Primes Diverges" Mathematics 8, no. 9: 1414. https://doi.org/10.3390/math8091414

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