Erdős problem 971 · problems.science

Let p(a, d) be the least prime congruent to a (mod d). Does there exist a constant c > 0 such that for all large d, p(a, d) > (1 + c) * φ(d) * log d for ≫ φ(d) many values of a?

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FormalConjectures/ErdosProblems/

971.lean

Retained formal statement3 of 3

Erdős [Er49c] proved that for any ε > 0 we have p(a, d) < ε * φ(d) * log d for ≫_ε φ(d) many values of a (for all large d).

[Er49c] Erdős, P., _On some applications of Brun's method_. Acta Univ. Szeged. Sect. Sci. Math. (1949), 57--63.

FormalConjectures/ErdosProblems/971.leanErdos971.erdos_971.variants.many_small5 linesExact file

1∀ ε > 0,2  ∃ C > 0,3    ∀ᶠ (d : ℕ) in Filter.atTop,4      C * ↑d.totient ≤5        ↑{a ∈ Finset.Iio d | a.Coprime d ∧ ↑(Erdos971.leastCongruentPrime a d) < ε * ↑d.totient * Real.log ↑d}.card

SolvedStatement only, no proof

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