Prime pairs (Q2878169)

This is a short note (in Dutch) written at the time that an important improvement on the existence of infinitely many prime pairs of the form \(\{p,p+d\}\) for a fixed \(d\) occurred (for \(d=2\) we have the famous conjecture about the existence of infinitely `classical' prime pairs).NEWLINENEWLINEAfter the development during the last decennial is explained, the important improvement due to \textit{Y. Zhang} [Ann. Math. (2) 179, No. 3, 1121--1174 (2014; Zbl 1290.11128)] is discussed: there are infinitely many prime pairs of the form \(\{p,p+d\}\) for a \(d\) with \(d<7\cdot 10^7\). The proof did not use any unproven conjecture (as was done in results by previous authors).NEWLINENEWLINEA more recent paper, discussing subsequent developments is due to \textit{A. Granville} [Bull. Am. Math. Soc., New Ser. 52, No. 2, 171--222 (2015; Zbl 1319.11064)] and for even more recent results on the size of the bound for \(d\) is covered on the website NEWLINE\url{http://www.michaelnielsen.org/polymath1} and then go to Polymath8 in the list on this page.