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-i>Pn j where n≥N, N is a large enough value and i, j are natural numbers?
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.
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