Anish Sola's Conjecture of Primes: A Universal Representation of Natural Numbers via Differences of Prime Powers

This work introduces Anish Sola’s Conjecture of Primes, a new assertion in number theory:Every natural number n≥1n \geq 1n≥1 can be expressed as n=pa−qbn = p^a - q^bn=pa−qb, where ppp and qqq are distinct primes, aaa and bbb are non-negative integers with a≠ba \neq ba=b, and the convention r0=1r^0 = 1r0=1 holds.The conjecture has been computationally verified for all integers up to 5000 with no counterexamples. This claim, if proved, would constitute a new representation theorem in number theory, connecting to Pillai’s problems, Catalan’s theorem, exponential Diophantine equations, and conjectures such as abc. The work discusses its novelty, potential uses, and future directions. sorry its aldready there by hans theorem 1974