Pythagorean Sieve. An ordered generator of odd primes and direct computation of the n-th prime.

Recursive modular sieve on the inradius index r. Exact characterization and ordered generation of odd prime numbers.Segmented algorithm acting on r instead of x. Reduced memory footprint in practical implementations, often by an order of magnitude compared to classical array-based sieves, thanks to segmentation on the r-variable. Direct computation of the n-th prime without precomputing all previous primes. This version provides supplementary computational verification materials associated with the Python reference implementation of the Pythagorean Sieve. It includes explanatory notes, performance notes, FAQ material, verification tables, sample outputs, a manifest, and SHA-256 checksums. This version does not contain source code, executable binaries, compiled libraries, or proprietary/enterprise material. Associated publication: R. Amato, "A Pythagorean Sieve and a Recursive Modular Characterization of Odd Primes", International Journal of Applied Mathematics, Vol. 38, No. 12s (2025), DOI: 10.12732/ijam.v38i12s.1467https://doi.org/10.12732/ijam.v38i12s.1467. Zenodo-enabled release. This release is identical in code to v1.0.0 and is issued to enable DOI minting via Zenodo for citation and archival purposes.