Erdős problem 1055 · problems.science

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 $r$ .

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FormalConjectures/ErdosProblems/

1055.lean

Retained formal statement2 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. If $p_r$ is the least prime in class $r$ , then how does $p_r^{1/r}$ behave? Erdos conjectured that this tends to infinity.

FormalConjectures/ErdosProblems/1055.leanErdos1055.erdos_1055.variants.erdos_limit1 lineExact file

1Filter.Tendsto (fun r => ↑(Erdos1055.p r) ^ (1 / ↑↑r)) Filter.atTop Filter.atTop

OpenStatement only, no proof

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