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In this paper it was shown that all prime numbers lie on 96 half-lines. Atthe same time, it was shown that if a given number does not lie on any of theabove half-lines, then it is a composite number. A corresponding linearmathematical relationship was also derived and it was shown that all primenumbers must satisfy it. If a given number does not satisfy the abovedependence, then it is a composite number. One linear equation and 8 numbersare enough to carry out all of the above-mentioned analyses. In addition, theastonishing cyclical nature of the occurrence of composite numbers in the setof natural numbers has been demonstrated.

Linearity of the position of prime numbers. The order of prime and composite numbers