应用逐步形成连续合数点去证明格林姆猜想（英文）.pdfVIP

Prove Grimm’s Conjecture by Stepwise Forming Consecutive Composite Number’s Points Abstract Regard positive integers which have a common prime factor as a kind, then the positive half line of the number axis consists of infinitely many recurring line segments which have same permutations of χ kinds of integer’s points, where χ≥1. Thus, the author first makes a positive half line of the number axis, yet the positive half line is marked only with integer’s points. Then, change gradually symbols of each kind of composite number’s points thereon according to the order of common prime factors from small to large, so as to form consecutive composite number’s points within limits that proven Bertrands postulate restricts to prove Grimm’s conjecture. AMS subject classification: 11A41; 11P82; 11B99 Keywords: consecutive composite numbers; distinct prime factors; Bertrand’s postulate; the number axis Contents 1. Introduction……………… ………………………….………………..P 2 2. Confirming Length of Consecutive Composite NumbersP3 P D F I c e c r e a m P D F E d i t o r 1 P R O 3. Analyzing Integer’s Points Concerned at the Number Axis….……..P3 4. Forming Consecutive Composite Number’s Points…………..……P8 5. Pχα and Pχα+1 Exist Not in a String of Con