We present a novel approach to test-case generation that satisfies four white-box, path-based coverage criteria: Prime Path, Simple Cycle, Simple Path, and Edge-Acyclic Path. Our method builds on a modified version of Johnson algorithm and enables test cases to be generated incrementally and on demand, rather than requiring the entire test suite to be computed upfront. This streaming capability represents a substantial advancement over existing approaches, as it allows testers to begin executing and refining tests immediately, thereby significantly improving the efficiency of test design. Our solution is inherently memory efficient, as it does not store all discovered coverage items; instead, it retains only the minimal set of paths required to generate subsequent coverage items on the fly. As a result, the approach scales to arbitrarily large graphs. In addition, the algorithm gives testers explicit control over the size of the generated test suite by allowing them to restrict the number of cycles permitted in a test path. The approach is grounded in new theoretical insights, most notably a novel characterization of prime paths in terms of the strongly connected components of control-flow graphs. We complement these theoretical contributions with a practical implementation and a comprehensive empirical evaluation. The results demonstrate that our method not only outperforms existing techniques in terms of execution time and memory consumption, but also provides testers with a more flexible and efficient tool for achieving high coverage while substantially reducing test design overhead.

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