In the book, for the first time, a direct relationship is established between logic and primes. Although the multivalued logics of Lukasevich were the result of a refutation of Aristotle's argument, their functional properties are of a purely number-theoretic nature. The study of this fact made it possible to define the concept of a prime number in logical terms. There is a real opportunity to reveal the structure of the latter. As a result, primes can be represented as root trees.