The sums of prime components of composite numbers lead to primenumbers, a remarkable phenomena in number theory that is examined inthis paper. We present a constructive proof methodology to show thatadding the prime components of the resulting composite numbers iterativelyconverges to prime numbers for any composite number higher thanfour. By applying logical reasoning and the fundamentals of number theory,we prove that all prime numbers larger than three have a finite numberof ”prime friends,” or composite numbers whose prime factors add up tothe prime number itself. We reveal the method by which prime numbersemerge from this iterative process by analyzing partitions of primenumbers and applying the function 2k +3. This abstract summarizes ourinvestigation into the convergence of prime numbers through the sums ofprime factors of composite numbers, demonstrating a significant relationshipbetween primes and composites in number theory.NOTE : We have created the term ”prime friend”; it is not aterm found in the traditional lexicon of mathematics.