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A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms

机译:通过信息熵和可见性算法的D-Primes规律性的数值研究

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Let a d-prime be a positive integer number with d divisors. From this definition, the usual prime numbers correspond to the particular case d=2. Here, the seemingly random sequence of gaps between consecutive d-primes is numerically investigated. First, the variability of the gap sequences for d∈2,3,…,11 is evaluated by calculating the informational entropy. Then, these sequences are mapped into graphs by employing two visibility algorithms. Computer simulations reveal that the degree distribution of most of these graphs follows a power law. Conjectures on how some topological features of these graphs depend on d are proposed.
机译:让D-Prime成为D分配的正整数。根据这种定义,通常的素数对应于特定情况d = 2。这里,在数值上研究了连续D-Primes之间的看似随机的间隙序列。首先,通过计算信息熵来评估D 12,3,...,11的间隙序列的可变性。然后,通过采用两个可见性算法将这些序列映射到图表中。计算机模拟表明,大多数这些图表的程度分布遵循权力法。提出了这些图表的一些拓扑特征依赖于D的猜想。

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