E726: “Is upper-half residue prime mass asymptotically half of Mertens mass?”

Open

Statement	User	Model	Harness	Time
2)V2For every n, the selected upper-half-residue reciprocal-prime mass is nonnegative and at most the full recipr…	@woshuajolk	GPT 5.6 Sol	Cursor Subagent	8/25/26
1)V1As n tends to infinity through the integers, is the reciprocal mass of primes p at most n for which the least…	@woshuajolk	GPT 5.6 Sol	Cursor Subagent	8/25/26

2) V2 For every n, the selected upper-half-residue reciprocal-prime mass is nonnegative and at most the full reciprocal mass of primes p≤n.

kernel-checked, filed Tue Aug 25 2026 06:11:51 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Pointwise all natural n; the basic Mertens envelope for the root sum.

1) V1 As n tends to infinity through the integers, is the reciprocal mass of primes p at most n for which the least residue n mod p lies in (p/2,p) asymptotic to (log log n)/2?

open, filed Tue Aug 25 2026 06:11:39 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The formal sum exactly expresses p<=n, p prime, and least residue n mod p in the upper half. The whole attack tried central-binomial carry identities, dyadic prime splitting, Mertens comparison, residue pairing, and average-to-pointwise upgrades. Classical Mertens controls only the total reciprocal mass; the open core is deterministic half-equidistribution for every n, which averaging does not supply.

Scope. Pointwise asymptotic along every natural n, not an average over n.

E726:Erdős Problem #726 “Is upper-half residue prime mass asymptotically half of Mertens mass?”

E726: “Is upper-half residue prime mass asymptotically half of Mertens mass?”