Erdős problem 1055

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. Show that for each $r$ there exists a prime $p$ of class $r$ .

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

1055.lean

Retained formal statement1 of 4

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?

FormalConjectures/ErdosProblems/1055.leanErdos1055.erdos_10551 lineExact file

1∀ (r : ℕ+), {p | Nat.Prime p ∧ Erdos1055.IsOfClass r p}.Infinite

OpenStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures4
statement retained
VibeMathed0
not observed here
PLBY Lean proofs0
not observed here
Jayyhk Erdős Lean0
not observed here
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki0
not observed here
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 1055.lean4