Prime quintuplets and the sextuplet boundary for Q(n)=n^47-(n-1)^47 (Titan Project, Part III). Exact Bateman-Horn singular series via Dirichlet L-functions mod 47; parameter-free prediction of 7 quintuplets / 0 sextuplets up to 2e11; first sextuplet expected near N*~1e13. Paper, data, scripts. v2 DOI 10.5281/zenodo.23178170
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