分数、整数和自然数中的素数

P. Mazurkin, P. Mazurkin
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引用次数: 0

摘要

素数序列在三个层次的数集(N)(Z)(Q)中被考虑,其中-自然数集(PN)中的素数序列,-整数集(WPN)中的整数素数序列,-有理数(分数)数集(FPN)中的有理数序列。在数列和横坐标上取整数的完整数列,对于素数数列,x轴的正右侧取自然数数列。证明了FPN集合在笛卡尔坐标系的象限中包含四种类型,WPN集合包括两条镜像相对的直线(左一在象限II和IV中,右一在象限I和III中)。从下一项WPN和序列的前一分量的PN中减去新的增量序列。从十进制到二进制的转换给出了级数WPN和PN,以及它们的增量,黎曼ζ函数在二进制展开的第二个垂直方向上的有理根1/2。这样的变换可以得到将原级数划分为块的块结构WPN和PN,然后得到从数字2开始的群。以编号为8168的块为例,我们证明了用可变振幅和振荡周期的孤波(孤子)形式的非对称小波,从2开始将群分解为单独的量子,最大相对误差为0.1%。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Prime Numbers Among Fractional, Integer and Natural Numbers
Series of primes are considered in three levels of sets of numbers (N)(Z)(Q), where – series of prime numbers in the set of natural numbers (PN), – a series of integer primes in the set of integers (WPN), – a series of rational primes in the set of rational (fractional) numbers (FPN). In series and the abscissa is taken as a complete series of integers , and for a series of prime numbers the positive right side of the x-axis is taken as a series of natural numbers . It is proved that the FPN set contains four types in the quadrants of the Cartesian coordinate system, the WPN set includes two mirror-opposite lines (the left one in quadrants II and IV and the right one in quadrants I and III). Subtraction from the next term WPN and PN of the previous component of the series gives new series of increments. Converting from decimal to binary gives for the series WPN and PN, as well as their increments, the rational root 1/2 of the Riemann zeta function on the second vertical of the binary expansion. Such a transformation makes it possible to obtain the block structure WPN and PN of partitioning the original series into blocks, and then the groups starting from the number 2. Using the example of block No. 8168 for the series PN, we proved the decomposition of groups into separate quanta, starting from the number 2, by asymmetric wavelets in the form solitary waves (solitons) with variable amplitude and oscillation period with a maximum relative error of 0.1%.
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