BGP246 Prime Gap & Formal Proof Explorer

1. Multidimensional Selberg Sieve & Spectrum Bound: H ≤ 246

Tuple Size k: 50 Sieve Dimension m: 5 Cutoff Degree °: 4

Scrub Range Base N [1 to 10,000]: 1..1200

Admissible Diameter

246

Variational Ratio M

2.084 > 2.0

Recurrent Gaps

≤ 246

Formal Status

Verified

Admissible k-tuple $\mathcal{H} = \{h_1,\dots,h_k\}$ mod Small Primes:

{0, 4, 6, 10, 12, 16, 22, 24, 28, 30, 36, 40, 42, 46, 52, 54, 58, 60, 66, 70, 72, 76, 82, 84, 88, 90, 94, 100, 102, 106, 108, 112, 118, 120, 124, 126, 130, 136, 142, 144, 148, 150, 156, 160, 162, 166, 172, 174, 178, 246}

2. AxiomProver AST Formal Deduction Tree 12/12 Steps Checked

Lean 4 AST Goal State / Lemma Certificate:

theorem BGP246_bounded_prime_gaps :
  ∃ H ≤ 246, ∃ᶠ (n : ℕ) in at_top, (prime (n + H) ∧ prime n) := by
  apply maynard_tao_sieve_admissible (k := 50) (H := 246)
  · exact polymath8b_admissible_50
  · exact selberg_variational_mass_gt_two (deg := 4)
        