formal-conjectures · wikipedia · ams-11
The Elliott–Halberstam conjecture: for every $\theta < 1$ and $A > 0$ there exists a
constant $C > 0$ such that
$$\sum_{1 \le q \le x^{\theta}} E(x; q) \le \frac{C x}{\log^A x}$$
for all $x > 2$.
Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).
Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.
Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Elliott%E2%80%93Halberstam_conjecture
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/ElliottHalberstamConjecture.lean
Local target: Corpus.WikipediaElliottHalberstamConjecture.elliott_halberstam
Source SHA-256: 7e03953894ed0c92add0b672c146fa68de20aebf9891d62d35c219f0f786e295
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.
Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.
The Elliott–Halberstam conjecture: for every $\theta < 1$ and $A > 0$ there exists a constant $C > 0$ such that $$\sum_{1 \le q \le x^{\theta}} E(x; q) \le \frac{C x}{\log^A x}$$ for all $x > 2$.
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No public records on this page.