For n∈ N, let P(n) mean 2<n quadandquad forall k∈ N,; 0<k land 2^k<n Longrightarrow n-2^k is prime. Is the set of natural numbers n satisfying P(n) infinite?

Erdős Problem #1142 — Prime Differences from Powers of Two

For $n\in\mathbb N$ , let $P(n)$ mean

2<n\quad\text{and}\quad \forall k\in\mathbb N,\; 0<k\ \land\ 2^k<n\ \Longrightarrow\ n-2^k\text{ is prime}.

Is the set of natural numbers $n$ satisfying $P(n)$ infinite?

References

Posted 1 month ago · edited 3 weeks ago

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