Briefly

Twin prime numbers

Twin prime numbers

We know that there cannot be two consecutive prime numbers, except for the pair {2, 3}. This is obvious if we think that in any pair of consecutive numbers, one of them will be even. And the only even prime number is 2. Now we consider the following: are there two consecutive odd ones that are cousins?

For example. even pairs {3, 5}, {5, 7}, {11, 13}, {17, 19} are made up of consecutive prime and odd numbers. It is precisely called twin cousins ​​to two prime numbers that differ in two units, as in the examples we have just seen. That is, they are of the form {p, p + 2}.

The first to call them "twin cousins" was Paul Stackel (1892-1919). Look at the following series with the first pairs of twin prime numbers:

{29, 31}, {41, 43}, {59, 61 }, {71, 73}, {101, 103}, {107, 109}, {137, 139}, {149, 151}, {179, 181}, {191, 193}, {197, 199}, {227, 229}, {239, 241},…

What is the next pair of twin prime numbers?

Solution

{281, 283}

It is believed that there are infinite twin cousins. But until today it is still unknown if it is true. The largest pair of twin cousins ​​known to date is (33,218,925) x 2 ^ 169,690 - 1 and (33,218,925) x 2 ^ 169,690 + 1