The OEIS A107311 conjectures are false: zeros of the prime zeta function accumulate up to sigma_c = 1.77954465354699... rather than x* = 1.72864723899818..., but kill condition 2 fired because Belovas, Cepaityte and Sabaliauskas 2025 Theorem 1 already owns the threshold by the same argument.
hunts/prime_zeta_rightmost (Record 43 of 98 in chronological sequence)
Guiding Question
Is x* = 1.7286... (root of zeta(x)=2) an upper bound for the real parts of the zeros of the prime zeta function and all prime-subset Dirichlet series, as OEIS A107311 conjectures, or is the true supremum sigma_c = 1.7795... (root of P(sigma) = 2^(1-sigma))?
Method & Verification
Both backends (python-flint at 350 bits and mpmath.iv at dps 40, with exact Fraction endpoint logic) decided sigma_c, x*, and the subset constant sigma_3, then a literature search fired MISSION.md kill condition 2 and reclassified the core as rediscovery.
Lineage & Relationships
None
Primary Sources (at pin 8fa46e134)
Editorial Notes
No HANDBACK.json at the pin. Headline filled from the rewritten RESULTS headline and the case log, not from the RESULTS H1 title. Case-log status is settled, kill condition 2 fired. Disposition maps settled to completed. The OEIS refutation and the tail-subset unboundedness corollary remain this hunt's own; the threshold theorem is rediscovery.
Date Provenance
commit 8b815e58afd90f7acc464c0c4b04f733c2d72bb9, hunts/prime_zeta_rightmost/RESULTS.md, author 2026-08-20T21:25:57-05:00