\documentclass[12pt,reqno]{article} \pagestyle{empty} \usepackage[usenames]{color} \usepackage{amssymb} \usepackage{graphicx} \usepackage{amscd} \usepackage[colorlinks=true, linkcolor=webgreen, filecolor=webbrown, citecolor=webgreen]{hyperref} \definecolor{webgreen}{rgb}{0,.5,0} \definecolor{webbrown}{rgb}{.6,0,0} \usepackage{color} \usepackage{fullpage} \usepackage{float} \usepackage{graphics,amsmath,amssymb} \usepackage{amsthm} \usepackage{amsfonts} \usepackage{latexsym} \usepackage{epsf} \setlength{\textwidth}{6.5in} \setlength{\oddsidemargin}{.1in} \setlength{\evensidemargin}{.1in} \setlength{\topmargin}{-.1in} \setlength{\textheight}{8.4in} \newcommand{\seqnum}[1]{\href{https://oeis.org/#1}{\underline{#1}}} \thispagestyle{empty} \begin{document} \begin{center} \epsfxsize=4in \leavevmode\epsffile{logo129.eps} \vskip 0.5cm \end{center} \theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{conjecture}[theorem]{Conjecture} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \begin{center} \vskip 0.7cm{\LARGE\bf Corrigendum: Upper Bounds for Prime Gaps \\ \vskip .1in Related to Firoozbakht's Conjecture } \vskip 0.7cm \large Alexei Kourbatov\\ www.JavaScripter.net/math\\ 15127 NE 24th St., \#578\\ Redmond, WA 98052 \\ USA\\ \href{mailto:akourbatov@gmail.com}{\tt akourbatov@gmail.com} \end{center} \vskip .2 in \section{Corrigendum}\label{corrig} The proof of Theorem 3 in [K], as well as subsequent discussion, should reflect the true range of applicability of Eq.~(11), necessitating the following changes (see [A]): \medskip\noindent In inequality (11), replace ``$x\ge5.43$'' with ``$x\ge 2634800823$'' \medskip\noindent Remove ``Let $k>9$.'' after inequality (11). \medskip\noindent In inequalities (12) and (13), remove ``for $p_k\ge29$''. \medskip\noindent Replace the last two sentences of the proof of Theorem 3 with \smallskip\noindent{\footnotesize Now, exponentiation with base $p_k$ yields (1) for $p_k\ge 2634800823$. This completes the proof since for $p_k\in[29,2634800823]$ both (1) and (10) hold unconditionally. } \medskip\noindent In the 2nd display formula on p.\,5, replace ``$x\ge5.43$'' with ``$x\ge 2634800823$'' . \medskip\noindent These changes have been incorporated in the arxiv paper arXiv:1506.03042v4. \medskip\noindent \centerline{{\bf References} } \smallskip\noindent [K] A.~Kourbatov, Upper bounds for prime gaps related to Firoozbakht's conjecture, {\it Journal of Integer Sequences}, {\bf 18} (2015), Article 15.11.2. \smallskip\noindent [A] C.~Axler, Corrigendum to ``New bounds for the prime counting function'', {\it Integers} {\bf 16} (2016), A22, 15 pp. \url{http://math.colgate.edu/~integers/vol16.html} \end{document} .