⌘+K

Pulse Explore Communities Researchers Journals

Home Communities Explore

July 21, 2026Open Access

Maynard's Sieve Refines Prime Gaps to 246, Not Yet Twin Primes — E8 Intelligence Research

Andrew Stewart Caldin

View Full Paper

Ask AI

Bookmark

Share

Key Points

The aim is to refine the GPY sieve to show bounded gaps between prime numbers and explore implications for twin primes.
Refined the GPY sieve to demonstrate gaps between primes; unconditional bound reduced to 246.
Utilized a multidimensional sieve weight defined by a variational problem.
Employed an optimal constant arising from the Selberg sieve involving admissible tuples.
Confirmed that there are infinitely many primes with a gap ≤ 246.
Showed that achieving twin primes (gap 2) requires a minimum of 2 admissible tuples, which yields a ratio < 1.
Highlighted the absence of direct geometric ratios in the sieve weights.

No abstract yet

We only have this paper's title and publication details.

Read it at the source→

Implication

Explores prime gaps, showing bounded gaps ≤ 246, suggesting pathways toward twin primes.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a61af56faa9903c5116a2ca https://doi.org/10.5281/zenodo.21467304

View Full Paper

Ask AI

Bookmark

Share

Keep reading

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Maynard's Sieve Refines Prime Gaps to 246, Not Yet Twin Primes — E8 Intelligence ResearchOriginal Research · 2026
2Maynard's Sieve Bounds Prime Gaps to 246, Twin Primes Require Stronger Conjecture — E8 Intelligence ResearchOriginal Research · 2026
3Maynard's Multidimensional Sieve: Bounded Prime Gaps from 70M to 246, Conditionally 6 — E8 Intelligence ResearchOriginal Research · 2026
4Bounded Prime Gaps at 246, but Twin Prime Conjecture Remains Unproven — E8 Intelligence ResearchOriginal Research · 2026
5Bounded Prime Gaps: Progress Toward, Not Proof of, the Twin Prime Conjecture — E8 Intelligence ResearchOriginal Research · 2026

Bounded Gaps ≤246 Proven, But Twin Prime Conjecture Remains Open — E8 Intelligence Research2026
Bounded Gaps in Primes: Progress, Not Proof, on Twin Prime Conjecture — E8 Intelligence Research2026
Bounded Gaps of 246, Not 2: The Unproven Twin Prime Conjecture — E8 Intelligence Research2026