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Forum: Computer Science & Computational Number Theory

2021-12-14, 17:20

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

As I just learned, mathematics professor Andreas...

As I just learned, mathematics professor Andreas Weingartner from Southern Utah University, Cedar City, Utah, USA has proven the following:

lim n-> infinite Wo(n) / (0.612415 .... * x / ln x) =...

Forum: Computer Science & Computational Number Theory

2021-11-01, 23:11

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

Thanks very much. That's right; a randomly drawn...

Thanks very much. That's right; a randomly drawn natural number n has approximately ln ln n + O (1) prime factors, where the standard deviation is O ((ln ln n) ^ 0.5). The number of all natural...

Forum: Computer Science & Computational Number Theory

2021-08-18, 08:55

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

You can find our last article on Minimum at the...

You can find our last article on Minimum at the following link, Page 57 - 66:

https://moodle.phst.at/pluginfile.php/308884/course/section/54892/006d1ba42c_SdW_highlights_201502_ges.pdf

The...

Forum: Computer Science & Computational Number Theory

2021-08-17, 00:34

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

In this post we will compare the Nullwertzahlen...

In this post we will compare the Nullwertzahlen with the prime numbers. In particular, it is also about the comparison of the functions Pi (x) and W0(x).

Pi (x) is the number of prime numbers less...

Forum: Computer Science & Computational Number Theory

2021-08-12, 13:02

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

Theorem of value restriction of sufficiently...

Theorem of value restriction of sufficiently large potencies:

n is a natural number with n >= 2

Then applies

W (nk) = 0 for all k > = ln n / ln 2 - 1 if n is even
W (nk) = 1 for all...

Forum: Computer Science & Computational Number Theory

2021-08-10, 22:02

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

Many Thanks. You are right, your algorithm is...

Many Thanks. You are right, your algorithm is better with a running time of O (n * ln ln n) than our algorithm with a running time of O (n * ln n).

Our algorithm differentiates between a...

Forum: Computer Science & Computational Number Theory

2021-08-10, 12:58

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

To give you a feeling how the distribution of...

To give you a feeling how the distribution of the numbers is developing, I give you the function values for all powers of ten from 1 to 12.

W0(10): 3
W1(10): 6
W2(10): 0
W3(10): 0
W4(10): 0

Forum: Computer Science & Computational Number Theory

2021-08-09, 23:54

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

Yes that is correct. 106 is a Zweiwertzahl...

Yes that is correct. 106 is a Zweiwertzahl (two-valued number). In the Minimum theory we write W (106) = 2.
106 is the 14th Zweiwertzahl. There are 27 Zweiwertzahlen up to 200:

19, 29, 38, 43,...

Forum: Computer Science & Computational Number Theory

2021-08-08, 20:36

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

I have only given the number 13356 as an...

I have only given the number 13356 as an introductory example. This posting is not a Minimum match!

If you subtract n - 2, this counts as n - 2 moves!

You cannot divide n by n, because the...

Forum: Computer Science & Computational Number Theory

2021-08-08, 17:19

Replies: 22

Minimum (Number Theory Game)

Views: 8,533

Posted By ThomasK

Minimum (Number Theory Game)

Minimum (Number Theory Game)

In spring 1983 a couple of school friends asked me to define a number theory game that has very simple rules, but is also very complex. So in April 1983 I defined...

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