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3月, 2024の投稿を表示しています

Pólya conjecture

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10=2*5 There are 2 prime numbers which are called prime factorization. This is n=50. 4=2^2 is 2 prime numbers. 12=2^2*3 is 3 prime numbers. I put even numbers in 1. There are 21 in 50. According to Pólya conjecture, there are more odd numbers in prime factorization. Prime numbers are chaotic , so this conjecture isn't fractal like piling squares. 906,150,257 ≤ n ≤ 906,488,079 There are more even numbers in n. It is hard to put circles in the square. I think that you need to adjust the range of the square to extinguish the circle, such as 906000000≦n≦906500000. For example, there are 7 even numbers in 4≦n≦16. This is contradictory.

Wolstenholme's theorem

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p is a prime number (p≧5). When p is 5, p^3=125. 2376 is one more than a multiple of 125. 2376=125*19+1 When p is 7, p^3=343. 1716 is one more than a multiple of 343. This is chaotic, but you can find it by your spreadsheet . Moreover, this is Binomial coefficient. Pascal's triangle is well known as fractal. This is harmonic numbers. You see that this is almost zeta function . Riemann's zeta function is ζ(s)=0.