Classification of natural numbers based on arithmetic progressions with a difference 6.

Ryabov G.G., Serov V.A.

The article considers a classification of natural numbers based on the submission of the set of all natural numbers as union of six infinite arithmetic progressions. The classes themselves (bijective to the progressions) are considered as members of two finite semigroups with regard to the operations of addition and multiplication. The binary relations between classes and examples of natural numbers properties at such classification are given.

Keywords: Arithmetic progression, bijection, binary relations, classification, Goldbach prime, set of natural numbers, semigroup.