Saturday, July 21, 2018

Gaps between primes

Everyone has probably learned in mathematics at school what primes are. They are numbers that are divisible only by 1 and themselves. So all the numbers that are divisible by 2 are missing.

Twin prime

While many primes are still close together for small numbers, separated by "even numbers", this becomes rarer as the number grows. For example, numbers less than 10 contain quite a few primes, so called twin primes which stand "side by side", separated only by even numbers. Like 2, 3, 5, and 7. The bigger the number, the less likely it is. For example, between 400 and 410, there are only the primes 401 and 409.

Cryptography uses primes to encrypt files and other data. For this large primes are used. Powerful computers are set to find ever larger primes, which turns out to be more and more difficult.

On the other hand, the question arises as to whether it is probable that, according to the currently largest prime number found, there are numbers that follow (after an even number) two prime numbers. Since there are an infinite number of numbers, I suspect that will eventually apply. Or maybe not? Nobody will have an answer for that until proven.