OAI/NumberTheory/TotientAsymptotic/TerminalPrimeGap.lean
3 declarations, 0 contain sorry, 0 declared as axioms
A valid Ford row forbids three consecutive equal positive coordinates.
- lemma
OAI.TotientAsymptotic.ford_first_two_coefficient_sumline 10 - lemma
OAI.TotientAsymptotic.ford_row_forbids_flat_tripleline 15 - lemma
OAI.TotientAsymptotic.terminal_strict_prime_gapline 48Source documentation
At one of the last two boundaries there is a strict prime gap, and the residual largest coordinate is exactly the final one.
lemma terminal_strict_prime_gap {x : ℝ} {n L : ℕ} (hL : 3 ≤ L) (hpos : 0 < fordPrimeCoordinate n L) (hrow : fordRowSum L (fordPrimeCoordinate n) (L-2) ≤ xi x (L-2)*fordPrimeCoordinate n (L-2)) : ∃ j : ℕ,L-1 ≤ j ∧ j ≤ L ∧ fordPrime n j < fordPrime n (j-1) ∧ fordPrimeCoordinate n j=fordPrimeCoordinate n L := by …Mentions: OAI.TotientAsymptotic.L, OAI.TotientAsymptotic.fordPrimeCoordinate, OAI.TotientAsymptotic.fordRowSum, OAI.TotientAsymptotic.xi, OAI.TotientAsymptotic.fordPrime