{"schema":"vela.problem-packet.v0.1","problem":997,"statement":"Call $x_1,x_2,\\ldots \\in (0,1)$ well-distributed if, for every $\\epsilon>0$, if $k$ is sufficiently large then, for all $n>0$ and intervals $I\\subseteq [0,1]$,\\[\\lvert \\# \\{ n<m\\leq n+k : x_m\\in I\\} - \\lvert I\\rvert k\\rvert < \\epsilon k.\\]Is it true that, for every $\\alpha$, the sequence $\\{ \\alpha p_n\\}$ is not well-distributed, if $p_n$ is the sequence of primes?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}