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
Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to cert...Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.展开更多
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
Suppose thatλ_(1),λ_(2),λ_(3),λ_(4),λ_(5)are nonzero real numbers,not all of the same sign,andλ_(1)/λ_(2)is irrational and algebraic.Let V be a well-spaced sequence,δ>0.In this paper,it is proved that,for ...Suppose thatλ_(1),λ_(2),λ_(3),λ_(4),λ_(5)are nonzero real numbers,not all of the same sign,andλ_(1)/λ_(2)is irrational and algebraic.Let V be a well-spaced sequence,δ>0.In this paper,it is proved that,for anyε>0,the number of v∈V with v≤N such that the following inequality|λ_(1)p_(1)~2+λ_(2)p_(2)~2+λ_(3)p_(3)~4+λ_(4)p_(4)~4+λ_5p_5~4-v|<v^(-δ)has no solution in prime variables p_(1),p_(2),p_(3),p_(4),p_(5)does not exceed O(N^(29/32+2δ+ε)).展开更多
This year marks the 50th anniversary of China-Thailand diplomatic relations as well as the“Golden Jubilee of China-Thailand Friendship.”From February 5 to 8,Thai Prime Minister Paetongtarn Shinawatra made an officia...This year marks the 50th anniversary of China-Thailand diplomatic relations as well as the“Golden Jubilee of China-Thailand Friendship.”From February 5 to 8,Thai Prime Minister Paetongtarn Shinawatra made an official visit to China.On February 8,the two sides issued the Joint Statement between the Government of the Kingdom of Thailand and the Government of the People’s Republic of China on Advancing the Comprehensive Strategic Cooperative Partnership and Building a Thailand-China Community with a Shared Future for Enhanced Stability,Prosperity,and Sustainability through a Forwardlooking and People-Centred Vision.展开更多
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
Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all re...Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all real numbers N1_(1)and N_(2)satisfying N_(1)>N_(1)^((0)),N_(2)>N_(2)^((0))andα≤N_(2)/N_(1)^(d=c)≤β,the system of two Diophantine inequalities|p_^(1)+…+p_(6)^(c)-N_(1)|<N_(1)^(−(1=c)(14=13−c))logN_(1),|p_(1)^(d)+…+p_(6)^(d)|N_(2)^(−(1=d)(14=13−d))logN_(2)has solutions in prime variables p_(1)…,p6.展开更多
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
建立了一种PRIME HLB固相萃取结合高效液相色谱-串联质谱法测定禽蛋中林可霉素残留的分析方法。样品经1%氨化乙腈提取,涡旋、振荡、超声处理后,再进行高速低温离心,Oasis PRIME HLB固相萃取柱净化。收集全部流出液经氮气吹干,复溶,供液...建立了一种PRIME HLB固相萃取结合高效液相色谱-串联质谱法测定禽蛋中林可霉素残留的分析方法。样品经1%氨化乙腈提取,涡旋、振荡、超声处理后,再进行高速低温离心,Oasis PRIME HLB固相萃取柱净化。收集全部流出液经氮气吹干,复溶,供液相色谱质谱分析。结果表明,林可霉素在1~50 ng·mL^(-1)线性关系良好,相关系数r为0.9993。方法定量限为1.0μg·kg^(-1),加标回收率为76.5%~93.3%,相对标准偏差为4.91%~8.57%。该方法准确性较好,可满足禽蛋中林可霉素的日常检测。展开更多
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
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.
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
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
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
The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is dis...The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is discussed. Through the corresponding prime distribution rate of integers and composite numbers, it is found that the corresponding prime distribution rate of composite numbers approaches the corresponding prime distribution rate of integers. The distribution principle of corresponding prime number of composite number is proved. The twin prime distribution theorem is obtained. The number of twin prime numbers is thus obtained. It provides a practical way to study the conjecture of twin prime numbers.展开更多
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
文摘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.
基金Supported by the Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0884)。
文摘Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.
文摘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.
基金Supported by NSFC(Nos.12301006,12471009,12071238,11901566,12001047,11971476)Beijing Natural Science Foundation(No.1242003)。
文摘Suppose thatλ_(1),λ_(2),λ_(3),λ_(4),λ_(5)are nonzero real numbers,not all of the same sign,andλ_(1)/λ_(2)is irrational and algebraic.Let V be a well-spaced sequence,δ>0.In this paper,it is proved that,for anyε>0,the number of v∈V with v≤N such that the following inequality|λ_(1)p_(1)~2+λ_(2)p_(2)~2+λ_(3)p_(3)~4+λ_(4)p_(4)~4+λ_5p_5~4-v|<v^(-δ)has no solution in prime variables p_(1),p_(2),p_(3),p_(4),p_(5)does not exceed O(N^(29/32+2δ+ε)).
文摘This year marks the 50th anniversary of China-Thailand diplomatic relations as well as the“Golden Jubilee of China-Thailand Friendship.”From February 5 to 8,Thai Prime Minister Paetongtarn Shinawatra made an official visit to China.On February 8,the two sides issued the Joint Statement between the Government of the Kingdom of Thailand and the Government of the People’s Republic of China on Advancing the Comprehensive Strategic Cooperative Partnership and Building a Thailand-China Community with a Shared Future for Enhanced Stability,Prosperity,and Sustainability through a Forwardlooking and People-Centred Vision.
文摘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.
文摘Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all real numbers N1_(1)and N_(2)satisfying N_(1)>N_(1)^((0)),N_(2)>N_(2)^((0))andα≤N_(2)/N_(1)^(d=c)≤β,the system of two Diophantine inequalities|p_^(1)+…+p_(6)^(c)-N_(1)|<N_(1)^(−(1=c)(14=13−c))logN_(1),|p_(1)^(d)+…+p_(6)^(d)|N_(2)^(−(1=d)(14=13−d))logN_(2)has solutions in prime variables p_(1)…,p6.
文摘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%。
文摘建立了一种PRIME HLB固相萃取结合高效液相色谱-串联质谱法测定禽蛋中林可霉素残留的分析方法。样品经1%氨化乙腈提取,涡旋、振荡、超声处理后,再进行高速低温离心,Oasis PRIME HLB固相萃取柱净化。收集全部流出液经氮气吹干,复溶,供液相色谱质谱分析。结果表明,林可霉素在1~50 ng·mL^(-1)线性关系良好,相关系数r为0.9993。方法定量限为1.0μg·kg^(-1),加标回收率为76.5%~93.3%,相对标准偏差为4.91%~8.57%。该方法准确性较好,可满足禽蛋中林可霉素的日常检测。
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘The distribution of twin prime numbers is discussed. The research method of corresponding prime number distribution is proposed. The distribution of prime numbers corresponding to integers and composite numbers is discussed. Through the corresponding prime distribution rate of integers and composite numbers, it is found that the corresponding prime distribution rate of composite numbers approaches the corresponding prime distribution rate of integers. The distribution principle of corresponding prime number of composite number is proved. The twin prime distribution theorem is obtained. The number of twin prime numbers is thus obtained. It provides a practical way to study the conjecture of twin prime numbers.
文摘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.
