Extend Bertrand’s Postulate to Sums of Any Primes

doi:10.4236/oalib.1110986

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Open Access Library Journal 10 2023

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Extend Bertrand’s Postulate to Sums of Any Primes

DOI: 10.4236/oalib.1110986, PP. 1-4

Pham Minh Duc

Subject Areas: Number Theory

Keywords: Bertrand’s Postulate, Rosser’s Theorem, L’Hospital Rule, Prime Number

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Abstract

According to Bertrand’s postulate, we have P_n P_n≥P_{n 1}. Is it true that for all n>1 then P_n-1 P_n≥P_{n 1}? Then P_n P_n-i>P_{n j} where n≥N, N is a large enough value and i, j are natural numbers?

Cite this paper

Duc, P. M. (2023). Extend Bertrand’s Postulate to Sums of Any Primes. Open Access Library Journal, 10, e986. doi: http://dx.doi.org/10.4236/oalib.1110986.

References

[1]	Bertrand, J. (1845) M’emoire sur le nombre de valeurs que peut prendre une function quand on y permute les lettres qu’elle renferme. Journal de l’Ecole Royale Polytechnique Cahier, 30, 123-140.
[2]	Tchebichef, P. (1852) M’emoire sur les nombres premiers. Journal de Mathématiques pures et appliquées, 17, 366-390.
[3]	Ishikawa, H. (1934) über die Verteilung der Primzahlen. Science Reports of the Tokyo Bunrika Daigaku, Section A, 2, 27-40.
[4]	Rosser, J.B. and Schoenfeld, L. (1962) Approximate Formulas for Some Functions of Prime Numbers. Illinois Journal of Mathematics, 6, 64-94. https://doi.org/10.1215/ijm/1255631807

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