Direct Positional Detection of Composite Integers via Prefix-Suffix and Border-Center Criteria

We study a clean positional framework for detecting composite integers directly fromtheir decimal expansions. The method uses only two mechanisms: prefix-suffix cuts andborder-center decompositions. Its logical core is elementary: if a nontrivial divisor is sharedby the visible positional blocks of a decomposition, then it divides the whole integer. Norevealer multipliers, wheel reduction, or square elimination are used in the main framework. The main contribution is methodological rather than theorem-centric. We prove theelementary positional compositeness criteria and then test them computationally up to 108. In the tested range, the clean positional filter detects 81. 292489% of composite integers whileproducing no false positives among primes. Moreover, across ten consecutive blocks of length10⁷, the observed composite detection rate remains confined to the interval 80. 293465% –82. 130177%, with no visible downward trend up to 108. The paper does not claim a characterization of primality, nor an efficiency advantage overclassical methods. Rather, it isolates a direct internal-divisibility observable of compositenessand shows that this observable has strong large-scale empirical coverage.