This paper shows that prime numbers do not constitute an intrinsic riddle of the numerical world, but arise as a necessary structural consequence of additive growth in combination with reconstructive order. Rather than proposing new proofs or computational methods, the work provides a structural and epistemological clarification of why prime numbers have historically been perceived as chaotic or random. The analysis makes clear that this perception results from a conflation of generative and reconstructive levels. By clearly distinguishing between addition as a nature-grounded process of emergence and multiplication as a human practice of simplification and ordering, the classical prime number problem becomes visible as a misclassification. The work is intended as a conceptual and structural contribution to number theory. Notes on complementary works: The formal mathematical elaboration of the underlying structure can be found at: https://zenodo.org/records/17649211 An algorithmic and illustrative implementation is available at: https://github.com/syntaris/primes4everybody This is the English version; a German version is published separately.