• ### EVOLUTIONARY MATHEMATICS AND SCIENCE FOR ON THE TERMINAL VALUE DISTRIBUTION IN THE PROCESS OF SUCCESSIVELY SUMMING UP ALL PRIME FACTORS OF A GIVEN NATURAL NUMBER

Author(s):
Hung-ping Tsao
Editor(s):
Lawrence K Wang (see profile)
Date:
2022
Group(s):
Science, Technology, Engineering, Arts and Mathematics (STEAM), Science, Technology, Engineering and Mathematics
Subject(s):
Mathematics, Science
Item Type:
Book chapter
Tag(s):
mathematic education, prime number, prime factorization, terminal value, Process of successively summing
Permanent URL:
https://doi.org/10.17613/w6vh-ne05
Abstract:
Tsao, Hung-ping (2022). Evolutionary mathematics and science for On the Terminal Value Distribution in the Process of Successively Summing up all Prime Factors of a Given Natural Number. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 8D, August 2022; 40 pages. Lenox Institute Press, MA, USA. No. STEAM-VOL4-NUM8D-AUG2022; ISBN 978-0-9890870-3-2. ............ABSTRACT: I was debating which natural number is the most wonderful. There are two candidates. One is 142857 found in the pyramids of ancient Egypt, the other 2982868385 found in my recent research of triangular arrays. It is known that each natural number greater than 1 can be expressed as a unique product of prime numbers, namely the prime factorization. For example, 84=2×2×3×7. By summing up all prime factors of 84, we obtain 2+2+3+7=14. Since 14=2×7, we further sum up all prime factors of 14 to obtain 2+7=9. Since 9=3×3 and 3+3=6, we can continue the same process to finally come up with 6=2×3 and 2+3=5, which is a prime number. Accordingly, we obtain 5 to be the terminal value of 84. Using the above process of successively summing all prime factors of a given natural number, I tried to make my decision as to which of 142857 and 2982868385 is the most wonderful based on their terminal values: whichever is less is the most wonderful. I’ll let you find it out. Meanwhile, I am making the following conjecture. Conjecture: Withing a certain limit, the probability of 5 being the terminal number is about the same as the probability of 7, 11 or 13 being the terminal number, which is approximately equal to 0.3.
Notes:
Conjecture: Withing a certain limit, the probability of 5 being the terminal number is about the same as the probability of 7, 11 or 13 being the terminal number, which is approximately equal to 0.3.
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