A prime $p$ is in class $1$ if the only prime divisors of $p + 1$ are $2$ or $3$ . In general, a prime $p$ is in class $r$ if every prime factor of $p + 1$ is in some class $\leq r - 1$ , with equality for at least one prime factor.Are there infinitely many primes in each class? If $p_{r}$ is the least prime in class $r$ , then how does $p_{r}^{1/ r}$ behave?

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 the **Erdős–Selfridge classification** [[nomath]](often written “class $r+$”)[[/nomath]]. A convenient way to restate your recursive definition is:

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

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

candidate solution ↗

formal

AMS 11 · textbook (literature)

theorem exists_p (r : ℕ+) : ∃ p, p.Prime ∧ IsOfClass r p

formal-conjectures/1055.lean ↗

oeis

A005113 — Smallest prime in class n (sometimes written n+) according to the Erdős-Selfridge classification of primes.2,13,37,73,1021,2917,15013,49681,532801,1065601,8524807,68198461,545587687,1704961513,23869461181,288310406533,183317462

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open

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formal

oeis

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