Twin prime

Two primes that differ by exactly 2 are known as twin primes. The following are the smallest examples:
3, 5
5, 7
11, 13
17, 19
29, 31
41, 43

It is not known whether or not there are infinitely many pairs of twin primes. A natural attempt to prove that there are infinitely many twin primes is to consider the sum of reciprocals of all the twin primes $B=\frac{1}{3}+\frac{1}{5}+\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+\frac{1}{17}+\frac{1}{19}+\cdots$ . If $B=\infty$ , then there would be infinitely many twin primes. However, it turns out that $B<\infty$ , which proves nothing. The number B is called Brun's constant.

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Twin prime