Are there arbitrarily large sets $S \subset \mathbb N$ such that the set $\{1\} \cup S$ has no subset that sums to a prime number?
2026-04-12 11:33:17.1775993597
Sets with no Prime Number-Generating Subsets
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According to this sequence the answer is yes: http://oeis.org/A052349. On this page there is a proof due to Chris Nash that this sequence is infinite.