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	"review": true,
20	"approval": "first-time"
21	}