Problem Statement
Let $A$ be the set of all odd integers not of the form $p+2^{k}+2^{l}$ (where $k,l\geq 0$ and $p$ is prime). Is the upper density of $A$ positive?
Categories:
Number Theory Additive Basis Primes
Progress
Progress
- Crocker (1971): $\gg\log\log N$ such integers in $\{1,\ldots,N\}$
- Pan (2011): Improved to $\gg_{\epsilon} N^{1-\epsilon}$
Related
- OEIS: A006286
- Related: Problems #10, #11, #16
Source: erdosproblems.com/9 | Last verified: January 13, 2026