A Computer-Assisted Lower Bound for Covering Systems with Prime-Minus-One Moduli

This paper investigates whether there exists a distinct covering system whose moduli are all of the form (p-1), where (p\geq 5) is prime. The question remains open.

A computer-assisted partial result is established: if such a covering system exists and (L) denotes the least common multiple of its moduli, then
[
L\geq 393120.
]
The proof combines an exact reciprocal-sum sieve, parity-capacity inequalities, and finite forced-congruence certificates based on the Chinese remainder theorem. All computations use exact integer and rational arithmetic.

The accompanying source archive contains the LaTeX manuscript, compiled PDF, README file, and a standalone Python verification program that reproduces the complete finite computation. This result provides a rigorous lower bound and computational framework but does not claim to resolve the original existence question.