Erdős Problem #1139

Let $1\leq u_1<u_2<\cdots$ be the sequence of integers with at most $2$ prime factors. Is it true that\[\limsup \frac{u_{k+1}-u_k}{\log k}=\infty?\]

#1139: [Va99,1.4]

number theory | primes

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This page was last edited 23 January 2026.

External data from the database - you can help update this
Formalised statement? Yes
Related OEIS sequences: Possible

7 comments on this problem

Likes this problem	ebarschkis
Interested in collaborating	None
Currently working on this problem	None
This problem looks difficult	None
This problem looks tractable	TerenceTao, msawhney, Przemek
The results on this problem could be formalisable	None
I am working on formalising the results on this problem	None

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