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Research Article Open access CC BY 4.0

Some Consequences of Bertrand's Extended Postulate

Pham Minh Duc

Journal of Advances in Mathematics and Computer Science · pp. 1–5 · Published 18 Mar 2023

10.9734/jamcs/2023/v38i61763

Abstract

Bertrand's postulate establishes that for all positive integers n > 1 there exists a prime number between n and 2n. We consider a generalization of this theorem as: for integers n ≥ k ≥ 2 is there a prime number between kn and (k + 1)n? This is a generalization of Bertrand's postulate extended as proved at link 1706.01009.pdf. The example is deduced that there are at least k -1 prime numbers between n and kn where n, k is a positive integers greater than 1. Then we can prove a number of hypotheses and some properties below. And here are the consequences to be deduced from it.

Bertrand's extended postulate prime number integer

References (5)

  1. 1 On a New Method in Elementary Number Theory Which Leads to An Elementary Proof of the Prime Number Theorem [DOI]
  2. 2 Mémoire sur les nombres premiers.
  3. 3 On The Prime Numbers In Intervals [DOI]
  4. 4 On intervals (kn,(k+1)n) containing a prime for all n>1 [DOI]
  5. 5 Proof of Legendre's Conjecture [DOI]

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