SternPrime 2006-10-11 17:33:01 2006-10-11 17:33:01 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here If for a given prime number $q$ there is no smaller prime $p$ and nonzero integer $b$ such that $q = 2b^2 + p$, then $q$ is a \emph{Stern prime}. These primes were first studied by Moritz Abraham Stern, in connection to a lesser known conjecture of Goldbach's. Like other mathematicians of the time, Stern considered 1 to be a prime number. Thus his list of Stern primes read thus: 2, 17, 137, 227, 977, 1187, 1493. A century later the list has been amended to include 3 (as in A042978 of Sloane's OEIS) but no terms larger than 1493 have been found. The larger of a twin prime is not a Stern prime.