The Conjecture by Goldbach Has Being Conjectured as Following
downloadThe Conjecture by Goldbach Has Being Conjectured as Following The Scientific Philosophic Thought Mode ﹠. Its Logical Process of Certificate on “ The Even Numbers , Greater than or Equal to 6 , Can Be Expressed as the Sum of 2 Prime Numbers”. Aixinjiaoluo?Xi Guo-wei A.The conjecture by Goldbach , in which the even numbers , greater than or equal to 6 , can be expressed as the sum of 2 prime numbers , has certified actual ( or false ) that the mathematic base of development so far is not complete yet . “What’s the prime number ” is the most important reason ? Is the definition complete ? Is it accurate ? The former definition of prime numbers was “ A number with only 1 and its 2 whole factor numbers ” , only an academic terminology , indicating only the whole numbers construct of prime numbers , and mathematic motion of exactly divisible feature , without the sphere of motion and the margin of whole numbers , and their mathematic expression .So , this definition is of one logical implication with mathematic form . Further , searching for the essence of prime number is to seek for the law of prime numbers . This is the thinking preparation of knowing the core and solution of questions . The question has been turned back to the year before 2200 when Euclidean earlier put an algorithm of “ try to find a common formula and express the prime numbers , one by one ” , but failed . Secondly , the problem of “ the even numbers , greater than or equal to 6 , can be expressed as the sum of 2 prime numbers ” just goes opposite of expressions in the formal mathematic relation with non-formal mathematic relation , as if the soul has left the body , with no expression . Further more , the whole numbers in the world does not exist single . I think that , numbers are produced of motion , both substantial and non-substantial , and their motion can be expressed in quantity and has the relation with mathematics , and the relation of theirs is called “Math . is the symmetry of the world ”. The whole numbers are only tiny spots mixed in the sea of all kinds of numbers , and vast numbers are of decimals and irrational numbers , and the problems are how we select the whole numbers from them , which are in the movement process of whole numbers we need , and The third reason , how to resolve the points of view of inlimity . The infinity and inlimity have 4 class names in 2 directions : They are the absolute infinity and absolute infinitesimal ( which are facing the bigger and the smaller ) , and relative infinity and relative infinitesimal , 2 kinds . The former 2 are the idea of real world , which are so far ,beyond the expression of math. to touch ,and the infinity ﹠ infinitesimal expressed by math are relatives . The [ a , b ] in the definite integral y= in which [ a , b ]intervals in the x axis are divided into infinite small intervals , which are the infinite small subintervals moving to the smaller direction , relatively , the fixed intervals [ a , b ] are infinity . While the motion signs mean moving to smaller and trending to infinitesimals , though [ a , b ] are in closed intervals , no variables , relatively , the [ a , b ] intervals are formed relative infinity in the intervals , then the infinity numbers and the infinitude numbers are naturally in the relative infinity [ a , b ] . Actually , the above is the point of view of inlimity of dialectical world . 1. The implication of proposition with formal question and unity . 2. Where are the prime numbers found with the definite of prime numbers expressed by math .？ What are its sphere and motion margin ? and 3. To set up the dialectical point of view of inlimity , after the philosophic concept of the above 3 ideas is set up , and opened B.“ The articles on law of prime numbers and odd composite numbers ” (//http: www.yundonglun.com ) has got the formula of prime number definition ,and solved the unity relation of logical implication and mathematic form , and the questions about sphere and motion margin of prime numbers and the fact of the prime number exists only in the relative infinity . Now let’s set up the formula of the prime numbers and the odd composite numbers in the most direct logical process of philosophy and search for the network station www.yundonglun.com - the math. process of inference or “The Doctorate Network . Forum on Prime Numbers cn. ” (1)identity ( principal of conservation ) r=r ( r is an odd number ) (2) expanse the sphere of motion of the number “ r ”. (3)change the expressive form , and see its motion margin , be an integer : ——(r) =Lr are called “ Lucas numbers ” , always be positive integers . a positive integer . a decimal . When , the odd number “r” is a prime number . When 1﹤ ﹤r , the odd number “ r ”is an odd composite number . (4) The definition formula of prime numbers , When =1 , 1= Lr - rmr —( =1)1.2 1=r△r- =1 is the efficient necessary condition of the odd number “ r ”fixed in the field of the prime numbers , which is called “ main element of formula of definitions of prime numbers ” and the number “ 1 ”(= ) is the characteristic number of the prime numbers . (5)The general significance and special significance and their nature of the smallest unit “ 1” ( positive ), and “-1” (negative) of the integers : 1、In the general sense , the numbers “1” and “-1”are the smallest counts and calculation units , positive or negative , of the integers , and take part in math. motion. 2、In the special sense , only when the formula of ( =1)1.2 is to hold water , the numbers “1”and “-1”are the main elements of definitions of the prime numbers , and take part in the math. motion . Conversely , if the numbers “1”and“-1”are the main elements of the definition of the prime numbers , then ( =1)1.2 formula can hold water . 3.The number “1” is the positive definite main element of the prime number “P” , and is the congruence with the number Lucas Lp as the modulus “P” , and conversely , “1” is the congruence with Lp, then the modulus “P”is the prime number , Lp 1(mod p) , and 4.If the number “-1” is the negative definite element of the prime number “P”, and the “-1”is the congruence with a–p number as the modulus “P ” . Conversely , if “-1”and “ ”are the congruence , then the P is the prime number . (mod p) , here C. The even number can expressed as the sum of 2 different odd numbers of “r” and “ ” 2n=r+1 (n=1,2,3……) = =n + n The “n” is cancelled , and the definite relation of the minimum even numbers of “2”: 2=1+1 such , make the definition in which the even numbers “2”are the sum of the minimum units of “1”of 2 integers , and also consists of sum of the main elements of the two prime numbers . When the formula 2r-2=rmr can hold water , the odd number “r” is the prime number , in which “m” is the positive integer , should be written: In same time are 2r=rmr+2 2r=2(mod r) 2 r=r(mr+1)+(2-r) 2=r×1+(2-r) When 2rand 2 are congruence the modulus “r” is the prime number , This is the special feature of the number “2” , (See for reference 《The Law of the Prime Number and Odd Composite Number 》,http://www.yundonglun .com) The different prime numbers “ ”also 2 = +2 can hold water : 2 2 (mod ) D.According to the above formula ( =1)1.2 and the main elements of the prime numbers the practical application and practice of the all features of the prime numbers as examples : For example 1: (1)The mathematic relations and its nature of the sum of even numbers “2” indicating the main elements of the prime numbers mean that : 2 1=Lr-rmr ——(d)1-1 + 1= ——(d)1-2 (2)The (d)1-1 multiplied by an odd number r(≥3) and (d)1-2 multiplied by an odd number l (≥3) , their sum is 2n: 2n (n=3,4,5……) r=rLr-r2mr ——（d）2-1 + = - 2 ——（d）2-2 If the two odd numbers “r” , and 1 in the 2 formulas（d）2-1 and （d）2-2 meet the formula ( =1)1.2 , then “r” and “1” are the prime numbers , certificating as the following : The solution of （d）2-1 is : in the same theorem : the definite formula of the prime number ,is ( =1)l mean that “r” and “1” meet the formula ( =1)1 of the definition of the prime numbers , and “r” and “1”are the prime numbers . (3)If the following two formulas meet the definitions of the prime numbers , then the two odd numbers “r” and “1” are the prime numbers . rLr-r2m= ——(d)3-1 ——(d)3-2 The solution of (d)3-1 gives In the same theorem : mean that if r and 1 meet the formula ( =1)1 of the definition of the prime numbers , then the two odd numbers “r” and “1” are the prime numbers . (4)If the following two formulas meet ( =1)2 then the two odd numbers “r” and “1”are prime numbers . r=r2△r-ra-r + 2n Mean that : r= In the same theorem : = is the formula ( =1)2 of the definition of prime numbers meaning that :“r” and “1” meet the formula ( =1)2 of definition of the prime numbers . (5):If the following two formulas meet the formula ( =1)2 of the definition of prime numbers , then the “r” and “1” ,two odd numbers ,are the prime numbers . Mean that : in the same theorem : = mean that : The r and 1 , two odd numbers , meet the formula ( =1)2 of the definition of the prime numbers . (6)The conclusion 1.The basic even numbers (minimum even numbers) 2 is the sum minimum units of 1 of two integers, and the minimum integer “1”is the basic unit of the integers , and the main elements of the prime numbers also . 2.The above confirms together that the minimum even numbers 2 has the basic meaning of the sum of two prime numbers and 3.The conjecture of “the even numbers ,greater than , or equal to 6 , can be expressed as the sum of the main elements of the two prime numbers .”has been certified actual . (7)The other solutions of above r and 1 in the all formulas are not effective solutions of the integers , no meaning at all . The above ex.2 has certified that “The odd number , greater than , or equal to 9 , can be expressed as the sum of three prime numbers ” . (n=4.5.6……) =Lp - pmp = =rLr-r2mr According to the ex. 1 , know that P= ( =1)1 the formula of the definition of prime numbers. and Mean that : “The odd numbers , greater than or equal to 9 ,can be expressed as the sum of three prime numbers .”