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erdős #1141

← #1140 · #1142 → (packet.json; erdosproblems.com)

Are there infinitely many $n$ such that $n - k^{2}$ is prime for all $k$ with $(n, k) = 1$ and $k^{2} < n$ ?

Worked, still open.

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

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formal

AMS 11 · solved (literature)

theorem erdos_1141 :
    answer(False) ↔ Infinite { n | Erdos1141Prop n }

formal-conjectures/1141.lean ↗

oeis

A214583 — Numbers m such that for all k with gcd(m, k) = 1 and m > k^2, m - k^2 is prime.3,4,6,8,12,14,18,20,24,30,32,38,42,48,54,60,62,68,72,80,84,90,98,108,110,132,138,140,150,180,182,198,252,318,360,398,468

links

have shown · paper

status

solved

finding.noted · reviewer:will-blair · 1 day

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