Goldbach conjecture proving coordinate plane demonstrator
A technology of Goldbach's conjecture and coordinate plane, which is applied to instruments, educational tools, teaching models, etc.
- Summary
- Abstract
- Description
- Claims
- Application Information
AI Technical Summary
Problems solved by technology
Method used
Image
Examples
Embodiment 1 1
[0131] Embodiment 1 An algorithm proof method
[0132] To prove Goldbach's conjecture with an arithmetic proof, the formula M=2a+2=2(x i +x j )+2=(2x i +1)+(2x j +1)=X i +X j ≥6,X i ≤X j , starting from the positive even number 6, write only one formula for each even number, and the proof process and conclusion obtained in turn are as follows:
[0133] From Goldbach's 2=1+1, 6=2x2+2=2x(1+1)+2=(2×1+1)+(2×1+1)=3+3;
[0134] From Goldbach's 3=1+2, 8=2x3+2=2x(1+2)+2=(2×1+1)+(2x2+1)=3+5;
[0135] From Goldbach 4=1+3, 10=2x4+2=2x(1+3)+2=(2×1+1)+(2×3+1)=3+7;... ....
Embodiment 2
[0136] Embodiment 2 Multiple arithmetic proof methods
[0137] To prove Goldbach's conjecture with multiple arithmetic proofs, the formula M=2a+2=2(x i +x j )+2=(2x i +1)+(2x j +1)=X i +X j ≥6,X i ≤X j , to prove Goldbach's conjecture, for positive even numbers greater than 4, the proofs can be written as multiple formulas. For example, if Figure 12 As shown, when x=22, Goldbach's 23=2+21=3+20=5+18=8+15=9+14, the even number 48 greater than 5 must be written as the addition of two odd prime numbers The 5 solutions are:
[0138] The first solution is: 48=2x23+2=2x(2+21)+2=(2x2+1)+(2x21+1)=5+43;
[0139] The second solution is: 48=2x23+2=2x(3+20)+2=(2x3+1)+(2×20+1)=7+41;
[0140] The third solution is: 48=2x23+2=2x(5+18)+2=(2x5+1)+(2×18+1)=11+37;
[0141] The fourth solution is: 48=2x23+2=2x(8+15)+2=(2x8+1)+(2×15+1)=17+37;
[0142] The fifth solution is: 48=2x23+2=2x(9+14)+2=(2x9+1)+(2×14+1)=19+29;.......
Embodiment 3
[0143] Example 3 Applying the dividing line to determine the scope of proof
[0144] The demonstration of the present invention compares and distinguishes the dividing line of the proof of the double base theorem and the dividing line of the proof of an arithmetic formula, and judges and proves the valid scope of Goldbach's conjecture, which is convenient for practical application.
[0145] Apply odd prime base number columns 1, 2, 3, 5, 6 to determine x n=6, in "Goldbach's Conjecture Coordinate Plane Demonstrator", looking down at the 6th row where the odd prime number base 6 in the first column of the table is located, it is known to apply the double-basis theorem to prove that the boundary line can be in the range of the closed interval [2, 7] Within, complete the summation of Goldbach bases 2, 3, 4, 5, 6, 7, prove that Goldbach’s conjecture is established on the closed interval [6, 16], find the solution of each even number, the number is the largest, And it is at least 1...
PUM
Login to View More Abstract
Description
Claims
Application Information
Login to View More 
PatSnap Eureka turns technology decisions into work you can execute. Powered by our Innovation Knowledge Graph, it runs expert workflows across engineering, life sciences, materials and intellectual property. Get your review-ready output in minutes.
