素整数与复合整数的Hexile筛分析
Hexile Sieve Analysis of Prime and Composite Integers
摘要：
在这里，我们展示了一个筛子分析素数和他们的复合材料，使用等价类的基础上，模6返回值适用于自然数。本文评述了这种“Hexile”筛的五个特点。第一个方面，是它将寻找素数的范围缩小到了自然数的三分之一。第二个特点是，我们可以从等价类公式中得到它的丢番图方程的一个性质，以区分素数和由这些素数相乘得到的合成。第三，我们可以从这些丢番图公式归因于一个非随机发生，不仅在两个等价类的复合材料，但默认情况下，作为一个结果：非随机发生的居民素数。第四，我们发展了筛选素数的理论基础。最后要提到的是，丢番图方程允许使用组合学或数值分析的另一条通向素数计数函数的途径。
英文摘要：
Here we demonstrate a sieve for analysing primes and their composites, using equivalence classes based on the modulo 6 return value as applied to the Natural numbers. Five features of this 'Hexile' sieve are reviewed. The first aspect, is that it narrows the search for primes to one-third of the Natural numbers. The second feature is that we can obtain from the equivalence class formulae, a property of its diophantine equations to distinguish between primes and composites resulting from multiplication of these primes. Thirdly we can from these diophantine formulations ascribe a non-random occurence to not only the composites in the two equivalence classes but by default and as a consequence : non-randomness of occurence to the resident primes. Fourthly we develop a theoretical basis for sieving primes. Of final mention is that the diophantine equations allows another route to a prime counting function using combinatorics or numerical analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
