New distance for any finite sets half the Hamming distance by J.K. Abdurakhmanov.pdf (257.19 kB)

# New distance for any finite sets, half the Hamming distance

In this paper, we introduce a new, previously unknown, distance (i.e., a new metric) in a set whose elements are some other (any) * finite* sets. It is proved that with such a metric the set under consideration is a metric space. A direct relationship is established between this distance and the Hamming distance: it is exactly two times smaller than the Hamming distance and it is much easier to calculate it. As an application, the set of natural numbers is considered as a discrete metric space with a new metric introduced, and a new

*criterion for the primality of a natural number is established.*

**metric**

**This is the first metric criterion in the history of mathematics for a natural number to be prime.**## History

## Email Address of Submitting Author

jamolidinkamol@gmail.com## Submitting Author's Institution

Andijan State University## Submitting Author's Country

- Uzbekistan