Erdős Problems

1,217 source-owned questions · 604 with a formal statement · searchable by statement, number, topic and source status.

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Source status, exact formal material, and reviewed Results are separate signals.

Open per source608
Resolved per source556
Other source status53

Exact formal statement available604 / 1,217

With Repository-reviewed evidence2 / 1,217

61 Problems

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Number	Question	Source says	Formal	Result here
#1059	Are there infinitely many primes $p$ such that $p - k!$ is composite for each $k$ such that $1 ≤ k! < p$ ?openFormalized	open	In Lean	No Result decision
#1137	Let $d_n=p_{n+1}-p_n$ , where $p_n$ denotes the $n$ th prime. Is it true that $\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$ as $x\to \infty$ ?openFormalized	open	In Lean	No Result decision
#1138	Erdős Problem 1138. Let $x/2 < y < x$ and $C > 1$ . If $d = \max_{p_n < x}(p_{n+1} - p_n)$ , where $p_n$ denotes the $n$ -th prime, then is it true that $\pi(y + Cd) - \pi(y) \sim \frac{Cd}{\log y}$ ?disproved (Lean)Formalized	disproved (Lean)	In Lean	No Result decision
#1139	Let $1\leq u_1 < u_2 < \cdots$ be the sequence of integers with at most $2$ prime factors. Is it true that $\limsup_{k \to \infty} \frac{u_{k+1}-u_k}{\log k}=\infty?$ openFormalized	open	In Lean	No Result decision
#1141	Are there infinitely many $n$ such that $n-k^2$ is prime for all $k$ with $(n,k)=1$ and $k^2 < n$ ?disproved (Lean)Formalized	disproved (Lean)	In Lean	No Result decision
#1142	Are there infinitely many $n > 2$ such that $n - 2^k$ is prime for all $k \geq 1$ with $2^k < n$ ?openFormalized	open	In Lean	No Result decision
#1143	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1184	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1187	No statement retained — open to read what the source holdssolvedNo formal declaration	solved	No formal statement	No Result decision
#1200	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1201	Is it true that for every $\epsilon,\eta>0$ there exists a $k$ such that the density of $n$ for which $P(n(n+1)\cdots(n+k))>n^{1-\epsilon}$ is at least $1-\eta$ (where $P(m)$ is the greatest prime divisor of $m$ )?openFormalized	open	In Lean	No Result decision
#1202	No statement retained — open to read what the source holdssolvedNo formal declaration	solved	No formal statement	No Result decision
#1212	Roughness criterion (sufficiency for the anchor conditions): if $a < s$ for all $s$ in the leg and the leg stays below $a + P^-(a)$ , then $a$ is coprime to the whole leg. Stated via divisibility: no prime factor of $a$ divides any $s$ with $a < s < a + p$ for all prime factors $p$ of $a$ .openFormalized	open	In Lean	No Result decision

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