Ivan Shishkin, Birch Grove

Théorème de Brun

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Théorème

La série des inverses des nombres premiers jumeaux est convergente vers la constante de Brun
B2≈1.90216...B_{2} \approx 1.90216.... C’est-à-dire

∑p,p+2∈P(1p+1p+2)=(13+15)+(15+17)+(111+113)+…<+∞\sum_{p,p+2\in \mathbb{P}}\left( \frac{1}{p}+\frac{1}{p+2}\right)=\left( \frac{1}{3}+\frac{1}{5}\right)+\left( \frac{1}{5}+\frac{1}{7}\right)+\left( \frac{1}{11}+\frac{1}{13}\right)+\ldots<+\infty

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