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 Showing results 1 to 11 of 11 Search took 0.01 seconds. Search: Posts Made By: ThomasK
 2022-08-12, 10:48 Replies: 42 Views: 35,627 Posted By ThomasK Congratulations on finding pi(10^29). I guess the... Congratulations on finding pi(10^29). I guess the computational effort for this is of the order of O(n^0.6). We are working on creating an total analysis for the minimum game up to 10^18. The...
 2021-12-14, 17:20 Replies: 22 Views: 9,178 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) =...
 2021-11-01, 23:11 Replies: 22 Views: 9,178 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...
 2021-08-18, 08:55 Replies: 22 Views: 9,178 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...
 2021-08-17, 00:34 Replies: 22 Views: 9,178 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...
 2021-08-12, 13:02 Replies: 22 Views: 9,178 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...
 2021-08-10, 22:02 Replies: 22 Views: 9,178 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...
 2021-08-10, 12:58 Replies: 22 Views: 9,178 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
 2021-08-09, 23:54 Replies: 22 Views: 9,178 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,...
 2021-08-08, 20:36 Replies: 22 Views: 9,178 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...
 2021-08-08, 17:19 Replies: 22 Views: 9,178 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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