The generalization and proof of Bertrand's postulate

George Giordano

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-3

Abstract:

The purpose of this paper is to show that for 0 < r < 1 one can determine explicitly an x 0 such that ∀ x ≥ x 0 , ∃ at least one prime between r x and x . This is a generalization of Bertrand's Postulate. Furthermore, the same procedures are used to show that if one can find upper and lower bounds for θ ( x ) whose difference is k x ρ then ∃ a prime between x and x − K x ρ , where k , K > 0 are constants, 0 < ρ < 1 and θ ( x ) = ∑ p ≤ x ln p , where p runs over the primes.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:907406

DOI: 10.1155/S0161171287000917

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