 Finally observe that \(\textit{element}(s,i)\) is equal to the smallest exponent \(n\) such that \(p_i^{n+1} \divides s\) but \(p_i^{n+2} \notdivides s\) and that such an exponent is also bounded by \(s\). We may thus provide a primitive recursive definition of \(\textit{element}(s,i)\) as follows: 