Number Theory

    

Prime Friends and the Sums of Prime Factors

Authors: Grgo Čolak

When the sum of the prime factors of a composite number n results in another composite number m, we can take the sum of the prime factors of m. We can see if that is equal to yet another composite number s, and so on. Given any composite number n being greater than four, do we end up with every prime number via the method explained before? We present a constructive proof of this problem using number theory and logic. We find out that every prime number greater than three has finitely many prime friends (composite numbers whose prime factors added are the prime number itself). This is demonstrated through the use of the function 2k+3 and the partitions of prime numbers. In this way we also learn that we always end up with prime numbers through the sums of prime factors of composite numbers.

Comments: 5 Pages.

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Submission history

[v1] 2022-04-14 01:00:02

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