Origin of Sexy Prime Numbers, Origin of Cousin Prime Numbers, Equations from Supposedly Prime Numbers, Origin of the Mersenne Number, Origin of the Fermat Number

We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.

Preliminary Identification of a Prime Number Other Than 2 and 3, the Origin of Twin Prime Numbers, the Structure of the Chain of Prime Numbers and the Set of Prime Numbers Less Than a Given Integer

The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it Esp. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted Enp. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted Ep. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.

How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)

Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.

PRiME HLB前处理技术联合超高效液相色谱-三重四极杆质谱系统检测水产品中17种磺胺类药物残留

使用通过型固相萃取小柱PRi ME HLB处理水产品样品,建立了一种水产品中17种磺胺类药物的简单、快速的筛选分析方法。水产品样品经80%乙腈水溶液(含0.2%甲酸)提取,过PRi ME HLB固相萃取柱净化,浓缩后经C_(18)色谱柱梯度洗脱分离,超高效液相色谱-三重四极杆质谱系统进行定量分析。结果表明,17种磺胺类药物在1.0~50.0 ng·mL^(-1)线性关系良好,相关系数R^(2)>0.99;该方法检出限为2μg·kg^(-1);添加浓度为10μg·kg^(-1)时方法回收率在71.3%~118.4%,RSD值均小于20%。

The Integral of the Inverse of the Primes

The present paper gives the proof of the set of primes as continuum and evaluates the analytical formula for the integral of the inverse of the primes over the distance. First it starts with the density of the primes, shortly recapitulates the prime-number-formula and the complete-prime-number-formula, the proof of the set of primes as continuum. The theoretical evaluation is followed in annexes by numerical evaluation of the theoretical results and of different constants, which represent inherent properties of the set of primes.

The Periodic Table of Primes

Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.

Distribution and Relation of Primes with Tesla Numbers 3, 6, and 9

This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.

Corresponding Prime Number Distribution Equation

The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.

PRiME HLB固相萃取结合UPLC-QTOF-MS测定烟液与烟丝中的依托咪酯

待测样品经乙腈提取后,使用PRi ME HLB固相萃取柱对样品提取液进行净化,经ACE EXCEL C18(2.1mm×50mm,2μm)色谱柱分离,以甲醇-5mmol·L^(-1)甲酸铵水溶液(含0.1%甲酸)作为流动相,梯度洗脱,采用电喷雾离子源正模式(ESI+),目标物二级离子模式(Targeted MS/MS)进行质谱分析。依托咪酯在2ng·m L^(-1)~200ng·m L^(-1)浓度范围内线性关系良好,相关系数r为0.999,在0.2μg·g^(-1),1.0μg·g^(-1),5.0μg·g^(-1)3个水平的加标回收率为86.6%~94.6%,RSD为3.1%~4.3%(n=9)。本方法具有操作简易快速、定性定量准确等特点。

On Perron’s Formula and the Prime Numbers

The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.

On the Number of Primes in the Interval (x, 2x) by an Elementary Method

An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2x]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation, and a tactical simplification of the terms gives rise to an expression whose verification envisages scope for its further studies.

PRiME HLB固相萃取-超高效液相色谱-串联质谱法测定水产品中的孔雀石绿含量

目的:建立了水产品中显色孔雀石绿(MG)及隐色孔雀石绿(LMG)残留量的超高效液相色谱-串联质谱测定方法。方法:样品用1.5%甲酸乙腈提取,离心,提取液经过PRiME HLB通过式固相萃取柱净化,氮吹后复溶,UPLC-MS/MS测定,同位素内标法定量。结果:在浓度为0.5~10.0μg/L范围内线性关系均良好,相关系数均大于0.995,检测限为0.008~0.01μg/kg,定量限为0.02~0.04μg/kg,加标回收率为86.8%~110.5%,相对标准偏差为1.6%~5.8%。结论:该方法高效快捷、准确可靠,能够满足大批量水产品中孔雀石绿及隐色孔雀石绿的检测。

Primetime Fashion Beijing hosts China Fashion Week A/W 2024

The China Fashion Week A/W 2024,hosted by the China Fashion Designers Association,took place in Beijing from March 23 to 31.Themed“Fu”(Empower),this season’s fashion week continued to focus on Chinese aesthetics,innovation in intangible cultural heritage,fusion of Chinese trends.

Proof of Concept for a Twin Prime Number Universe Using Set Theory

The Fine Structure Constant (eFSC) Model attempts to give a classical definition to a magical number that underlies much of quantum physics. The Fine Structure Constant (α) value equal to 137.03599206 represents a dimensionless constant that characterizes the strength of the electromagnetic (EM) interaction between subatomic charged particles. Python-generated property counts for the twin prime force F{139/137} show that the adjusted ratio gives a value of α = 137.036. This implies a mathematical framework underlying this constant is based on twin prime numbers and set theory. This study attempts to demonstrate a proof of concept that a hierarchy of fractional twin prime (αII) forces replicates the quantum nature of the universe and is aligned with the Standard Model of Particle Physics. An expanded eFSC Model demonstrates that twin prime forces and their property sets are mathematically viable substitutes for nuclear reactions, as demonstrated for the Beta-minus decay of neutrons into protons. Most significantly, the positive and negative prime numbers define these nuclear reactants and products as positive or negatively charged ions. Furthermore, the eFSC Model provides new insights regarding the hierarchy of EM forces underlying the quantum nature of the universe.

The Quantum Microverse: A Prime Number Framework for Understanding the Universe

This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.

安德里茨将向中顺洁柔宿迁基地提供两台Prime LineCOMPACT M紧凑型卫生纸机

安德里茨将向中顺洁柔位于江苏省宿迁市宿城区运河宿迁港产业园的生活用纸生产基地提供两台Prime LineCOMPACT M紧凑型卫生纸机。这两台纸机的最大运行车速可达1,650m/min,幅宽3.5m,以原生商品浆为原料,最大产能为94t/d,用以生产生活用纸原纸。两台纸机均配备了安德里茨先进的Prime系列产品,包括Prime Flow流浆箱,Prime Dry钢制扬克缸和Prime Dry Canopy通风式气罩等,并采用大直径高负荷真空压榨辊,确保在生产高品质纸品同时通过高效干燥方式实现低能耗生产。

On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors

This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.

The Primes and Their Subsets as Continuum like the Integers

The present paper gives the proof of the set of primes as a continuum. It starts with the density of the primes, and shortly recapitulates the prime-number-formula and the complete-prime-number-formula. Reflecting the series of the primes over any prime gives the double density of occupation of integer positions by the union of the series of multiples of the primes. The remaining free positions render it possible to prove Goldbach’s conjecture and the set of primes as a continuum. The theoretical evaluation is followed in annexes by numerical evaluation, demonstrating the theoretical results. The numerical evaluation results in different constants and relations, which represent inherent properties of the set of primes.

基于Vega Prime的无人直升机飞行模拟系统

以某型无人直升机为仿真对象设计了一款飞行模拟系统,该系统由飞行仿真模块、座舱仿真模块、视景仿真模块和控制台模块4部分组成。飞行仿真模块对旋翼、尾桨、机身、平尾、垂尾等各部件进行动力学建模,并使用S函数编写了Simulink模块;座舱仿真模块使用GL Studio软件设计了照片级的飞行仪表用于实时显示飞行数据;视景仿真模块是基于Vega Prime仿真平台二次开发的;采用基于MFC(microsoft foundation classes)的多线程方法搭建了基本的仿真框架并设计了控制台模块界面,可以用于和用户的实时交互。最后仿真验证了系统的可行性。

Supersemiprime Rings and Supersemiprime Radical

In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.