Abstract This paper presents a new structural-cyclic sieve for prime numbers, which is simpler and more visual than the classical Sieve of Eratosthenes. The method is based on a table with period 30, immediately excluding numbers divisible by 2, 3, and 5. The remaining numbers form eight infinite arithmetic progressions (corridors). For each prime key (starting from 7), composite numbers are generated by a linear formula: T × M + T × 30 × n. The spatial arrangement of composites within T rows forms a repeating template (colour stencil), which can be copied indefinitely without further multiplication. The algorithm is deterministic, easily parallelisable, and suitable for hardware implementation. Program verification up to 200,000 shows zero errors, confirming absolute accuracy.
Emma Helmdach (Wed,) studied this question.