A Pattern of Prime Numbers and its Application in Primality Testing

Primes are so unique and elegant that each of them has only two factors (1 and itself), and natural numbers with this property are sparse. In this study, we present a pattern of prime numbers by proving that C 2x+3y=p ∈Q and C 2x+3y=c ∈G, where p denotes the prime numbers and c denotes the composite numbers. x and y count the quantity of number 2 and number 3, respectively. C 2x+3y=p represents the channel of the function 2x + 3y = p. A channel is a trace of the function 2x + 3y = n in the first quadrant of the plane rectangular coordinate system. C 2x+3y=c is similar. Q and G are two sets with different types of channels. The proposed pattern of prime numbers also provides a way for primality testing, which is of significance to public-key cryptography.