Limits RegistryPUBLIC RECORD
Limits RegistryThe smallest gap between consecutive primes that recurs infinitely often is known to be at most 246 (Polymath8b, 2014), and trivially at least 2 for any prime pair other than (2,3) — the Twin Prime Conjecture asserts the true value is exactly 2.
The question, scope, and sources behind this Registry record.
The smallest gap between consecutive primes that recurs infinitely often is known to be at most 246 (Polymath8b, 2014), and trivially at least 2 for any prime pair other than (2,3) — the Twin Prime Conjecture asserts the true value is exactly 2.
Determine H1 = liminf_{n to infinity} (p_{n+1} - p_n), the smallest gap between consecutive primes that occurs for infinitely many n.
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
Current frontiers derived from accepted Claims.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
The frontier as it changed over time.
| Year | Bound | Value |
|---|---|---|
| 2026 | Lower bound | 2 |
| 2026 | Upper bound | 246 |
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.