Two primes ??are ??twin primes when its distance is 2.

(3, 5) (5, 7) (11, 13) (17, 19)(29, 31) (41, 43)… Are twin primes

Dubbed twins because of **Paul Stäckel**, the idea of twin primes is to find consecutive **odd** numbers (and primes??), as we know the only two consecutive primes are 2 and 3, so its distance is 2.

Thoose are of type **(6n – 1, 6n + 1)** for n> 1 which is reasonable since otherwise the two numbers would be even or one would be a multiple of 3.

How many twin primes not known to exist but the most common belief is that they are **infinite**.

Its distribution has been approximated by a **Hardy-Littlewood** conjecture and following a distribution law very similar to the prime number theorem.

We also know that the sum of the reciprocals of all twin primes converges in a constant called **Brun constant** unlike the sum of the primes that diverges.

*B*_{2} ˜ 1,902160583104

The largest known twin primes are far **2003663613 · 2 ^{195000}**

**– 1**and

**2003663613 · 2**

^{195000}**+ 1**, and were discovered by

**Vautier**,

**McKibbon**and

**Gribenko et al**in

**2007**.

Today it is known that a numbers **n** and **n + 2** are twin primes if and only if: