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?

Sources

Browse retained paths and inspect the exact material available for this Problem.

3 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

971.lean

Retained formal statement2 of 3

Erdős [Er49c] proved that the statement in erdos_971 holds for infinitely many values of 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.infinite_sequence6 linesExact file

1∃ c > 0,2  ∃ C > 0,3    {d |4        C * ↑d.totient ≤5          ↑{a ∈ Finset.Iio d |6                a.Coprime d ∧ ↑(Erdos971.leastCongruentPrime a d) > (1 + c) * ↑d.totient * Real.log ↑d}.card}.Infinite

SolvedStatement only, no proof

Sources

Search problems.science