User:CRGreathouse/Primes in polynomials
| Existence / density | Single polynomial | Multiple polynomials |
|---|---|---|
| Linear | Dirichlet's theorem (1837) / PNT in AP (1896) | Dickson's conjecture (1904) / — |
| Arbitrary degree | Bunyakovsky conjecture (1857) / ※ | Schinzel's hypothesis H (1958) / Bateman–Horn–Stemmler conjecture (1962) |
※ The Hardy–Littlewood conjectures F and K (1923) are special cases, quadratics and respectively, but the general case was not handled until subsumed by the conjecture of Bateman, Horn, & Stemmler.
