Let $α > 1$ be irrational. Are there infinitely many primes $p$ such that $⌊ p α ⌋$ is also prime?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **open in general** for a fixed irrational (\alpha>1).

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_972 : answer(sorry) ↔ ∀ α > 1, Irrational α → (primeSet α).Infinite

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