在整数之前定义素数：素数素数分布的第一性原理方法
Defining the prime numbers prior to the integers: A first-principles approach to the distribution of primes
摘要：
虽然从古希腊人开始，素数就一直受到数学研究的关注，但正如马库斯·杜·索图伊最近所说的那样，理解这些数字所积累的努力“并没有揭示素数的起源。“在这里，我们建议通过在自然数之前定义素数来解决这个长期存在的难题--这与素数的标准数论定义相反，在标准数论定义中，这些数字来自自然数。其结果是一个第一性原理的角度来看，暴露和解释的'起源'的分布和他们的数学属性，并提供了一个直观的，以及教学方法的素数与潜在的影响我们的思考这些古老的数学对象。这个观点的一些直接结果是算术算术基本定理的另一个证明，素数共享的概率模型以及解释它们的次随机相关结构，以及黎曼假设的等价公式。
英文摘要：
While the prime numbers have been subject to mathematical inquiry since the ancient Greeks, the accumulated effort of understanding these numbers has - as Marcus du Sautoy recently phrased it - 'not revealed the origins of what makes the primes tick.' Here, we suggest that a resolution to this long-standing conundrum is attainable by defining the primes prior to the natural numbers - as opposed to the standard number theoretical definition of primes where these numbers derive from the natural numbers. The result is a first-principles perspective on the primes that exposes and explains the 'origins' of their distribution and their mathematical properties and provides an intuitive as well as pedagogical approach to the primes with the potential to impact our thinking about these age-old mathematical objects. A few immediate outcomes of this perspective are another proof of the fundamental theorem of arithmetic, a probabilistic model of primes sharing as well as explaining their subrandom correlation structure, and an equivalent formulation of the Riemann hypothesis.
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