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Prime-representing polynomial systems in five variables

Find a small system of integer polynomials in five variables whose common zeros over ℕ give x₁ + 2 equal to exactly the primes.

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1{
2 "domain": "mathematics",
3 "topics": [
4 "number-theory"
5 ],
6 "type": "construction",
7 "source": {
8 "key": "frontiermath-open",
9 "name": "FrontierMath: Open Problems",
10 "url": "https://epoch.ai/frontiermath/open-problems/prime-generating-polynomials",
11 "id": "prime-generating-polynomials",
12 "curator": "Epoch AI",
13 "status": "unsolved",
14 "as_of": "2026-10-20",
15 "catalog": "0521c19bbd38"
16 }
17}