Each element has unique properties and if a number system was to be used to describe uniqueness, prime numbers stand out. Without uniqueness, the system would be chaotic. Using a numerical system analysis of seven chemically diverse elements (H, He, Ne, Ar, Kr, C, Fe) across 13 physical domains yields 91 and an additional 23 for 104 relationships the author found a prime number numeric pattern. Each reproducing measured NIST values within 0.5% error using rule based parameters, with median error of 0.020%; the maximum of 0.497%. The probability of this arising by coincidence is P ≈ 10⁻⁵oo — but this was reduced as the author found a pattern within the domain. A domain-prime table is established: each physical domain (viscosity, sound speed, ionization energy, thermal conductivity, etc.) possesses a characteristic base prime and denominator, invariant across all elements tested. The first four primes — 2, 3, 5, and 7 — account for all domain operators across all tested elements and properties. Here we demonstrate that the S-field encodes elemental identity through prime-number architecture — specifically, that measurable physical properties of elements are connected by prime-number operators derived exclusively from the prime factorizations of their atomic numbers.
Lyle Semple (Thu,) studied this question.