It is shown that in testing technique based on linear-feedback shift registers, the use of primitive polynomials in a signature-analysis register is not always better than using nonprimitive polynomials. The results show how some primitive polynomials may actually yield maximum aliasing errors. These results are based on the simulation of single stuck-at faults, but they also hold for certain multiple stuck-at faults. The best testing technique appears to be one that uses a binary counter in test-pattern generation with a primitive polynomial in signature analysis.