We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version of the conjecture which empirically demonstrates remarkable accuracy even for modest values of primes.

中文翻译：

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关于贝特曼-霍恩猜想的注释

我们报告了对 Bateman-Horn 猜想的实证研究结果。当所涉及的多项式不是单数时，该猜想以其众所周知的形式产生相当大的偏差。我们提出了该猜想的修改版本，即使对于中等的素数值，它也凭经验证明了显着的准确性。