Developed a new Almost Prime Numbers API for the leanprover-community/mathlib4 repository, introducing formal predicates to characterize numbers by their exact or maximal count of prime factors, including a dedicated semiprime definition. Leveraging Lean and formal verification techniques, the implementation utilized the Ω function to enable rigorous proofs of properties such as closure under multiplication and foundational cases for zero, one, and prime numbers. This work established an extensible framework for reasoning about prime-factorization depth within number theory, expanding mathlib4’s capabilities for future research and tooling. The contribution focused on robust, proof-driven design without addressing bug fixes during the period.