Wheel modulus ($W={\prod }_{p\in S}p$)

The wheel modulus is the product $W$ of a chosen finite set of small distinct prime numbers in wheel factorization. Except for those primes themselves, every prime candidate must lie in a residue class coprime to $W$. For $W=2\cdot 3\cdot 5=30$, the allowed residues are $1,7,11,13,17,19,23,29$, repeating every thirty integers. The proportion retained is $\phi (W)/W$. Passing the wheel only avoids these small divisors; it does not certify primality, since composite values such as $49$ still pass.