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Composite numbers in sumsets of sparse sets
Show that if A, B ⊆ {1,…,N} each have at least N^0.49 elements, then the sumset A + B contains a composite number.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "number-theory", | |
| 5 | + "combinatorics" | |
| 6 | + ], | |
| 7 | + "type": "proof", | |
| 8 | + "source": { | |
| 9 | + "key": "green-100", | |
| 10 | + "name": "Ben Green's 100 open problems", | |
| 11 | + "url": "https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.58", | |
| 12 | + "id": "58", | |
| 13 | + "curator": "Ben Green", | |
| 14 | + "poser": "Ben Green and Adam J. Harper", | |
| 15 | + "status": "open", | |
| 16 | + "as_of": "2026-10-20", | |
| 17 | + "catalog": "0521c19bbd38" | |
| 18 | + } | |
| 19 | +} | |