A Positive Integer 𝑵 Such That 𝒑𝒏 + 𝒑𝒏+𝟑 ~ 𝒑𝒏+𝟏 + 𝒑𝒏+𝟐 For All 𝒏 ≥ 𝑵

 Applied Mathematics and Sciences: An International Journal (MathSJ)

ISSN: 2349 – 6223

https://www.airccse.com/mathsj/index.html

September 2023, Volume 10, Number 3

A Positive Integer 𝑵 Such That 𝒑𝒏 + 𝒑𝒏+𝟑 ~ 𝒑𝒏+𝟏 + 𝒑𝒏+𝟐 For All 𝒏 ≥ 𝑵

Pham Minh Duc and Luong Van Tam, VNU University of Science, Vietnam

ABSTRACT

According to Bertrand's postulate,we have 𝑝𝑛 + 𝑝𝑛 ≥ 𝑝𝑛+1. Is it true that for all 𝑛 > 1 then 𝑝𝑛−1 + 𝑝𝑛 ≥𝑝𝑛+1? Then 𝑝𝑛 + 𝑝𝑛+3 > 𝑝𝑛+1 + 𝑝𝑛+2where 𝑛 ≥ 𝑁, 𝑁 is a large enough value?

KEYWORDS

Bertrand’s Postulate, Rosser's theorem, L’Hospital Rule, prime number

Original Source URL: https://www.airccse.com/mathsj/papers/10323mathsj01.pdf

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