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Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory 被引量:2
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作者 Silviu Guiasu 《Natural Science》 2019年第6期187-196,共10页
If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers... If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers with primes, during the prime factorization, may be viewed as being the outcome of a parallel system which functions properly if and only if Euler’s formula of the product of the reciprocals of the primes is true. An exact formula for the number of primes less than or equal to an arbitrary bound is given. This formula may be implemented using Wolfram’s computer package Mathematica. 展开更多
关键词 Goldbachs CONJECTURE Symmetric prime Cousins Systemic Approach in NUMBER Theory Parallel System Covering INTEGERS with primeS Eulers FORMULA for the Product of Reciprocals of primeS FORMULA for the Exact NUMBER of primeS Less than or Equal to an Arbitrary Bound
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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
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作者 Mady Ndiaye 《Advances in Pure Mathematics》 2024年第5期321-332,共12页
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 ... 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. 展开更多
关键词 Cousin prime Numbers Sexy prime Numbers Real Sexy prime Numbers Equations from Supposed prime Numbers Mersenne Number Fermat Number Supposed prime Numbers prime Numbers
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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
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作者 Mady Ndiaye 《Advances in Pure Mathematics》 2024年第1期30-48,共19页
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 ... 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 E<sub>sp</sub>. 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 E<sub>np</sub>. 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 E<sub>p</sub>. 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. 展开更多
关键词 Supposedly prime Numbers Non-prime Numbers prime Numbers prime Numbers Less Than a Given Integer prime Numbers between Two Given Integers
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The Proof of Goldbach’s Conjecture on Prime Numbers
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作者 Silviu Guiasu 《Natural Science》 2019年第9期273-283,共11页
Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly... Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well. 展开更多
关键词 PROOF of Goldbachs CONJECTURE Hidden Symmetry of primeS Matching primeS and Composite INTEGERS Arranging ODD INTEGERS in Frames The Existence and the Number of GOLDBACH Solutions
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Remarks on Goldbach’s Conjecture on Prime Numbers
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作者 Silviu Guiasu 《Natural Science》 2019年第12期336-344,共9页
The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact... The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes. 展开更多
关键词 The Existence and the Number of GOLDBACH Solutions The Proof of Goldbachs CONJECTURE Hidden Symmetry of primeS Matching primeS and ODD Composite INTEGERS Arranging ODD INTEGERS in Frames
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How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)
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作者 John Richard Wisdom 《Advances in Pure Mathematics》 2024年第4期228-241,共14页
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 , ... 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. 展开更多
关键词 Number Theory prime Number Groups Twin primes prime Structure and Sequence prime Subtraction and Addition
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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
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作者 安德里茨 《生活用纸》 2024年第7期77-77,共1页
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... 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。 展开更多
关键词 宿 prime 宿
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Creator和Vega Prime在数字城市规划中的应用 被引量:2
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作者 李粉莉 童小念 《计算机与数字工程》 2010年第12期154-156,共3页
Creator和Vega Prime的虚拟现实视景仿真平台具有快速处理复杂仿真事件的能力。为了构建一个虚拟仿真漫游系统,阐述Creator和Vega Prime在数字城市规划设计中的应用,基于Creator和Vega Prime实施武汉光谷广场的视景仿真漫游。实验结果表... Creator和Vega Prime的虚拟现实视景仿真平台具有快速处理复杂仿真事件的能力。为了构建一个虚拟仿真漫游系统,阐述Creator和Vega Prime在数字城市规划设计中的应用,基于Creator和Vega Prime实施武汉光谷广场的视景仿真漫游。实验结果表明,虚拟现实技术能够将城市规划工作从传统的平面静态层次提升到立体的动态层次。 展开更多
关键词 CREATOR VEGA Application 仿 仿 广
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On Perron’s Formula and the Prime Numbers
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作者 Michael M. Anthony 《Advances in Pure Mathematics》 2024年第6期487-494,共8页
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 form... 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. 展开更多
关键词 Perron Fixed Points ITERATIONS Number Theory Riemann Hypothesis ITERATIONS INVARIANCE primeS
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Proof of Concept for a Twin Prime Number Universe Using Set Theory
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作者 John R. Crary 《American Journal of Computational Mathematics》 2024年第3期305-317,共13页
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 di... 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. 展开更多
关键词 Fine Structure Constant (α) prime Numbers Set Theory Conceptual Model Quantum Physics Light and Matter Beta-Minus Decay
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The Integral of the Inverse of the Primes
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作者 Pal Doroszlai Horacio Keller 《Advances in Pure Mathematics》 2023年第5期250-266,共17页
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,... 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. 展开更多
关键词 Density of primes prime-Number-Formula Complete-prime-Number-Formula Goldbachs Conjecture Twin primes K-Tuples of primes primes as Continuum
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The Quantum Microverse: A Prime Number Framework for Understanding the Universe
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作者 John R. Crary 《American Journal of Computational Mathematics》 2024年第2期264-274,共11页
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... 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. 展开更多
关键词 Fine Structure Constant Fractional Coupling Constants Matter/Antimatter Dark Matter/Energy Quantum Gravity prime Numbers Set Theory
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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 被引量:2
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作者 余海芬 徐桦 +5 位作者 吴真善 包蔚 朱晓芸 何锴 黄忠 战涛 《现代食品》 2024年第1期213-215,224,共4页
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... 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%。 展开更多
关键词 prime HLB
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The Harmonic Neutron Hypothesis: Prime Number Factor Patterns and Their Relationship to the Hierarchy of the Fundamental Particles and Bosons 被引量:1
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作者 Donald William Chakeres Richard Vento 《Advances in Pure Mathematics》 2015年第5期240-250,共11页
The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial har... The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial harmonic fractional exponents, 1 ± (1/n), of a fundamental frequency, Vf. The goal is to evaluate the prime and composite factors associated with the neutron n0, the quarks, the kinetic energy of neutron beta decay, the Rydberg constant, R, e, a0, H0, h, α, W, Z, the muon, and the neutron gluon. Their pure number characteristics correspond and explain the hierarchy of the particles and bosons. The elements and black body radiation represent consecutive integer series. The relative scale of the constants cluster in a partial harmonic fraction pattern around the neutron. The global numerical organization is related to the only possible prime factor partial fractions of 2/3, or 3/2, as pairs of 3 physical entities with a total of 6 in each group. Many other progressively resonant prime number factor patterns are identified with increasing numbers of smaller factors, higher primes, or larger partial fractions associated with higher order particles or bosons. 展开更多
关键词 BOSON Fundamental PARTICLES prime Numbers Physical Constants Unification Models NEUTRON QUARKS Lepton W BOSON Z BOSON GLUON
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Distribution and Relation of Primes with Tesla Numbers 3, 6, and 9
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作者 Javier Mendoza-Navarrete Huetzin Perez +4 位作者 Ismael Ojeda Victor Verdugo Gabriel Luna Sandoval Ricardo Jimenez Garcia Jaime Alvarez 《Journal of Applied Mathematics and Physics》 2024年第4期1021-1027,共7页
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 Co... 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. 展开更多
关键词 Tesla Numbers prime Number Twin prime Numbers Twin Pair
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How to Check If a Number Is Prime Using a Finite Definite Integral
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作者 Jesús Sánchez 《Journal of Applied Mathematics and Physics》 2019年第2期364-380,共17页
In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain... In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will be commented on the paper, but a separate study will be needed to have detailed conclusions. Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved. 展开更多
关键词 PRIMALITY Test NUMBER Theory primeS FACTORIZATION Fourier Transform Parsevals Theorem Time DOMAIN Frequency DOMAIN Numerical Computation
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Corresponding Prime Number Distribution Equation 被引量:1
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作者 Dan Liu Chenglong Liu 《Journal of Applied Mathematics and Physics》 2023年第11期3354-3365,共12页
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 ... 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. 展开更多
关键词 prime Number Composite Number Twin prime Numbers Corresponding prime Distribution Equation Twin prime Inequality Function
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PRiME HLB固相萃取结合UPLC-QTOF-MS测定烟液与烟丝中的依托咪酯
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作者 王华 罗达龙 +5 位作者 覃蓝 莫惠欣 李媛捷 何姗珊 杨梓莹 刘虹虹 《分析仪器》 CAS 2024年第5期25-30,共6页
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... 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。 展开更多
关键词 prime HLB
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On the Number of Primes in the Interval (x, 2x) by an Elementary Method
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作者 Sudhindra B. Kittur 《Advances in Pure Mathematics》 2024年第1期16-29,共14页
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 nu... 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. 展开更多
关键词 prime Numbers Composite Numbers EXPRESSION INTEGERS
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The Periodic Table of Primes
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作者 Han-Lin Li Shu-Cherng Fang Way Kuo 《Advances in Pure Mathematics》 2024年第5期394-419,共26页
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... 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. 展开更多
关键词 primeS COMPOSITES the Periodic Table of primes
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