
A WELLROUNDED DISTRIBUTION OF SMALL PRIME NUMBERS AS TERMINAL VALUES IN THE PROCESS OF SUCCESIVELY SUMMING UP ALL FACTORS OF THE NATURAL NUMBERS
 Author(s):
 Hungping Tsao
 Editor(s):
 Lawrence K Wang (see profile)
 Date:
 2023
 Group(s):
 Science, Technology, Engineering, Arts and Mathematics (STEAM)
 Subject(s):
 Mathematics, Numbers, Prime, Numbers, Natural
 Item Type:
 Book chapter
 Tag(s):
 Prime number, Prime factor, Terminal value in the process of successively summing up prime factors, Twin primes sandwich, Ham sandwich
 Permanent URL:
 https://doi.org/10.17613/aw2zvs27
 Abstract:
 Hungping Tsao (2023). A Wellrounded Distribution of Small Prime Numbers as Terminal Values in the Process of Summing up all Factors of the Natural Numbers. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Lawrence K. Wang and Hungping Tsao (editors). 5(10D), October 2023; 59 pp. Lenox Institute Press MA, USA. tsaohp.tsao6@gmail.com ; doi.org/10.17613/aw2zvs27 ...... ABSTRACT: We provide here a new platform for exploring of prime numbers by defining the terminal value t(n) for each natural number n by successively summing up its prime factors. We further define two sets A={5} and B={7, 11, 13}. We shall call 5 the Aterminal value, 7, 11 or 13 a Bterminal value and all others Cterminal values. We have found, up to n =3002, 1 septuple (7 in a roll) Aterminal values ending at 2330, 1 septuple Bterminal values ending at 1595 and 3 sextuple (6 in a roll) Cterminal values ending at 1551, 2562 and 2986, respectively. We further spot checked around n = 10000 and found 1 nonuple (9 in a roll Cterminal values ending at 9787. We finally found that 60% (59%, respectively) of terminal values are 5, 7, 11 or 13 up to n = 2000 (3000, respectively) and came up with a good way of estimating such percentage p(n) by using twin primes, which will be called cheese sandwich if the terminal value of the number sandwiched in between twin primes in question is from C or ham sandwich otherwise. As it turned out, the percentage of ham sandwiches among twin sandwiches is a slightly less than p(n) for n = 2000 or 3000. CONJECTURE 1. In a long run, the percentage of single terminal values from A and B combined is slightly less than 60% and the percentages for double, triple and quadruple terminal values from A and B combined are 16%, 4% and 1%, respectively. CONJECTURE 2. There would not be any mtuple terminal values from A or B for m > 10. CONJECTURE 3. There might be some mtuple terminal values from C for m > 10.
 Notes:
 KEYWORDS: Prime number, Prime factor, Terminal value in the process of successively summing up prime factors, Twin primes sandwich, Ham sandwich, Cheese sandwich.
 Metadata:
 xml
 Published as:
 Book chapter Show details
 Pub. DOI:
 10.17613/aw2zvs27
 Publisher:
 Lenox Institute Press, MA, USA. Lenox.Institute@gmail.com
 Pub. Date:
 October 26, 2023
 Book Title:
 \"Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)\"
 Author/Editor:
 Lawrence K. Wang and Hungping Tsao (editors)
 Chapter:
 5(10D)
 Page Range:
 1  59
 ISBN:
 9780989087032
 Status:
 Published
 Last Updated:
 4 months ago
 License:
 All Rights Reserved

A WELLROUNDED DISTRIBUTION OF SMALL PRIME NUMBERS AS TERMINAL VALUES IN THE PROCESS OF SUCCESIVELY SUMMING UP ALL FACTORS OF THE NATURAL NUMBERS