Erdős problem 997 · problems.science

Is it true that, for every $\alpha$ , the sequence $\{ \alpha p_n\}$ is not well-distributed, if $p_n$ is the sequence of primes?

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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

997.lean

Retained formal statement2 of 3

He also claimed in [Er64b] to have proved that there exists an irrational $\alpha$ for which $\{\alpha p_n\}$ is not well-distributed. He later retracted this claim in [Er85e], saying "The theorem is no doubt correct and perhaps will not be difficult to prove but I never was able to reconstruct my 'proof' which perhaps never existed."

The existence of such an $\alpha$ was established by Champagne, Le, Liu, and Wooley [CLLW24].

FormalConjectures/ErdosProblems/997.leanErdos997.erdos_997.variants.irrational1 lineExact file

1∃ α, Irrational α ∧ ¬Erdos997.IsWellDistributed fun n => Int.fract (α * ↑(Nat.nth Nat.Prime n))

SolvedStatement only, no proof

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