Odious primes minus evil primes among first $n$ primes

formal-conjectures · oeis · ams-11

$a(n)$ is the number of primes with odd binary weight (odious primes) among the first $n$ primes
minus the number with even binary weight (evil primes).

Shevelev conjectures that $a(n) \ge 0$ for $n > 3$.

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://oeis.org/A130911
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/130911.lean
Local target: Corpus.OEIS130911.conjecture
Source SHA-256: b7d8b5693dbacacf0e788c0e14d55c80dd2784441a03ab66845a7c3bb7189c2e
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.

Public JSON record