Quantum Computation and Quantum Information $($Michael A$.$ Nielsen, Isaac L$.$ Chuang$),$ exercise$5\mathrm{.}18$: $($Factoring $91)$ Suppose we wish to factor N $=91.$ Confirm that steps $1$ and $2$ are passed. For step $3,$ suppose we choose x $=4,$ which is co$-$prime to $91.$ Compute the order r of x with respect to N$,$ and show that xr$/2$ mod $91=641($mod $91),$ so the algorithm succeeds, giving gcd$(641,19)=7.$