Primes p for which p − 2 has an odd number of prime factors

Prove that for infinitely many primes p, the number p − 2 has an odd number of prime factors counted with multiplicity.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"number-theory"
5	],
6	"type": "proof",
7	"source": {
8	"key": "green-100",
9	"name": "Ben Green's 100 open problems",
10	"url": "https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.64",
11	"id": "64",
12	"curator": "Ben Green",
13	"status": "open",
14	"as_of": "2026-10-20",
15	"catalog": "0521c19bbd38"
16	},
17	"review": true,
18	"approval": "first-time"
19	}