Current research on the distribution of prime numbers either narrows down to counting due to a focus on applied fields, meaning it only counts without knowing which numbers are prime, or it explores patterns but, because of a cause-from-effect order, leads to unclear results and only approximate rather than definitive distribution patterns. This paper attempts to discuss a common type of multiplication—multiplication whose factors do not contain 1, called skip-multiplication—introducing skip-numbers and skip-products, to explain the essence of prime numbers as full-skip numbers and their distribution patterns, and to achieve a fundamental grasp of prime numbers in terms of identity rather than merely quantity through the method of reverse selection from the skip-product table. Furthermore, because tables rely on enumeration, their role in application is at most auxiliary rather than a replacement for any tool; thus, this paper mainly provides a new number-theoretic understanding of prime and composite numbers in the pure mathematical theory domain. The appendix supplements some patterns of the skip-multiplication theory tables and discussions on the oddness of primes and the Riemann Hypothesis.