Mills常数的确定及关于Honaker问题的一个注记
Determining Mills' Constant and a Note on Honaker's Problem
摘要：
米尔斯在1947年证明，存在一个常数$A$，使$\lfloor A^{3^n} \rfloor$是一个素数的每一个正整数$n$。确定$A$需要在很短的时间间隔内确定一个有效的Hoheisel类型的素数结果--尽管大多数书都忽略了这个困难。在黎曼假设下，我们证明了每对连续立方体之间至少存在一个素数，并确定（给定RH）米尔斯常数$A$的最小可能值确实以1.3063778838开始。我们通过确定超过6000位数的相关素数和超过60000位数的可能素数（PRP）来计算这个值到6850个小数位。我们也适用于克莱默-格兰维尔猜想Honaker的问题在相关的背景下。
英文摘要：
In 1947 Mills proved that there exists a constant $A$ such that $\lfloor A^{3^n} \rfloor$ is a prime for every positive integer $n$. Determining $A$ requires determining an effective Hoheisel type result on the primes in short intervals - though most books ignore this difficulty. Under the Riemann Hypothesis, we show that there exists at least one prime between every pair of consecutive cubes and determine (given RH) that the least possible value of Mills' constant $A$ does begin with 1.3063778838. We calculate this value to 6850 decimal places by determining the associated primes to over 6000 digits and probable primes (PRPs) to over 60000 digits. We also apply the Cramér-Granville Conjecture to Honaker's problem in a related context.
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