The Bateman–Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green–Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau’s conjecture. We discuss the Bateman–Horn conjecture, its applications, and its origins.

中文翻译：

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Bateman-Horn猜想：启发式，历史和应用

Bateman-Horn猜想是关于素数分布的深远影响。它暗示了许多已知的结果，例如素数定理和Green-Tao定理，以及许多著名的猜想，例如孪生素数猜想和Landau猜想。我们讨论了Bateman-Horn猜想，其应用及其起源。