Brun's constant for prime quadruplets is the sum of the reciprocals of all prime quadruplets \begin{equation*} B_4 = \sum_{\substack{p\\p + 2 \text{ is prime}\\p + 6 \text{ is prime}\\p + 8 \text{ is prime}}} \left(\frac{1}{p} + \frac{1}{p + 2} + \frac{1}{p + 6} + \frac{1}{p + 8} \right)\approx 0.8705883800. \end{equation*} Viggo Brun proved that the constant exists by using a new sieving method, which later became known as Brun's sieve.