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Apr 25, 2020 at 14:55 comment added user142929 In past week I've removed the mentioned comment (as outdated). I'm sorry for my insistence in previous weeks and many thanks for your patience @GHfromMO
Apr 18, 2020 at 18:20 vote accept user142929
Mar 13, 2020 at 21:02 comment added user142929 Possibly unrelated to my question, is I think that a similar Firoozbakht's conjecture for Ramanujan primes maybe is feasible. I don't know if this proposal that I evoke have the best mathematical content and maybe it is in the literature, since I know that Zhi-Wei Sun studied in articles many similar inequalities involving arithmetic functions (I know his preprint in arXiv arXiv:1208.2683 of one of his papers, and I don't know if he, or other mathematician, studied the inequality that I evoke). Isn't required a response, just I add it if you want to think about it.
Feb 9, 2020 at 15:32 comment added GH from MO @user142929: I have no time for MO now. At any rate, I suggest that you ask this as a separate question.
Feb 6, 2020 at 12:15 history edited JoshuaZ CC BY-SA 4.0
Noting more recent bound per comment
Feb 6, 2020 at 8:08 comment added GH from MO Chudakov's bound was improved several times. Currently we know that $g_n=O(p_n^{21/40})$. This was proved by Baker-Harman-Pintz (2000).
Feb 4, 2020 at 18:40 comment added user142929 Many thanks for your nice answer. I'am going to study it, and as soon I can I'm going to upvote it. If you want feel free to add feeback about the second of the conjectures.
Feb 4, 2020 at 18:27 history answered JoshuaZ CC BY-SA 4.0