A Twin-Gap Existence Conjecture

Q: What does this research mean for the field?

Every large lower twin prime is conjectured to have a productive gap of size o(t), which yields a generative map on twin primes. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Dacomb Bierton

doi:10.5281/zenodo.22058356

August 22, 2026Open Access

A Twin-Gap Existence Conjecture

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Key Points

To establish a constructive refinement of the Twin-Prime Propagation Conjecture using bounded productive gaps.
Formulated a mathematical framework evaluating the spacing following lower twin prime values.
Defined asymptotic bounds of size o(t) to establish a generative mapping sequence across twin primes.
Conjectured that every sufficiently large lower twin prime contains a productive gap scaled to o(t).
Showed that the existence of such gaps produces a generative map that links twin prime pairs.

Implication

Theoretical analysis proposes a productive gap bound for twin primes, suggesting a generative map for prime pair propagation.

Abstract

Constructive refinement of the Twin-Prime Propagation Conjecture. Conjectures that every large lower twin prime has a productive gap of size o(t), yielding a generative map on twin primes.

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Cite This Study

Dacomb Bierton (2026) studied this question.

synapsesocial.com/papers/6a8c00d0bca056c88e6dfbd8 https://doi.org/10.5281/zenodo.22058356

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A Twin-Gap Existence Conjecture

Key Points

Implication

Abstract

Discussion

Cite This Study

A Twin-Gap Existence Conjecture

Key Points

Implication

Abstract

Discussion

Cite This Study

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