Erdős Problems

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

Add a contribution Collection details

Full distribution

Collection coverage

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

1,217 Problems · 2 with reviewed evidence

26/26

Number	Question	Source says	Formal	Result here
#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 $m$ )?Source says openFormalized	open	In Lean	No Result decision
#1202	No statement retained — open to read what the source holdsSource says solvedNo formal declaration	solved	No formal statement	No Result decision
#1203	Prove that $F(n)\to \infty$ as $n\to \infty$ .Source says openFormalized	open	In Lean	No Result decision
#1204	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#1205	No statement retained — open to read what the source holdsSource says solvedNo formal declaration	solved	No formal statement	No Result decision
#1206	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#1207	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#1208	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#1209	Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers which tends to infinity sufficiently fast. If there is an $n$ such that all $n+a_k$ are primes then must there exist infinitely many such $n$ ?Source says openFormalized	open	In Lean	No Result decision
#1210	Let $A\subseteq [1,n)$ be a set of integers such that $(a,b)=1$ for all distinct $a,b\in A$ . Is it true that $\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)$ ?Source says openFormalized	open	In Lean	No Result decision
#1211	No statement retained — open to read what the source holdsSource says solvedNo 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 $a$ .Source says openFormalized	open	In Lean	No Result decision
#1213	No statement retained — open to read what the source holdsSource says provedNo formal declaration	proved	No formal statement	No Result decision
#1214	Let $x,y\geq 1$ be integers such that, for all $n\geq 1$ , the set of primes dividing $x^{n}-1$ is equal to the set of primes dividing $y^n-1$ . Must $x=y$ ?Source says provedFormalized	proved	In Lean	No Result decision
#1215	No statement retained — open to read what the source holdsSource says disprovedNo formal declaration	disproved	No formal statement	No Result decision
#1216	No statement retained — open to read what the source holdsSource says disprovedNo formal declaration	disproved	No formal statement	No Result decision
#1217	No statement retained — open to read what the source holdsSource says provedNo formal declaration	proved	No formal statement	No Result decision