论文标题
legendre近似和算术偏见
The Legendre Approximation and Arithmetic Bias
论文作者
论文摘要
质数定理历史上的一个有趣的一集涉及Legendre提出的一个公式，以计算给定界面以下的素数。我们指出，算术偏见可能在达到该公式以及随后的几十年认可方面发挥着重要作用。我们还表明，Legendre Constant 1.08366满足了一定的简单自然标准，并且猜想该标准是Legendre如何在他的公式中达到错误的常数。
An interesting episode in the history of the prime number theorem concerns a formula proposed by Legendre for counting the primes below a given bound. We point out that arithmetic bias likely played an important role in arriving at that formula and in its subsequent widespread, decades-long recognition. We also show that the Legendre constant 1.08366 satisfies a certain simple and natural criterion, and conjecture that this criterion is how Legendre arrived at that erroneous constant in his formula.
