Consecutive Composite Representations of Primes: Experimental Structures, Exceptional Sets, and Weighted Corrections

This work presents computational experiments on additiverepresentations of prime numbers using consecutivecomposite sequences. Several structural phenomena are observed, including: - increasing representation density;- sparsity of exceptional primes;- multiple representation behavior;- weighted correction representations. Computational experiments were conducted up to 10^8. The work is exploratory and conjectural in nature,with emphasis on experimental structure discoveryin additive number theory.