On Twin Primes, Complementary Pairs, and the Distribution of Triangular Prime Arrays: Elementary Proofs Regarding the Goldbach Conjecture and the Twin Prime Conjecture

Author: Ding Daqian
Publisher:
Publish Date: 2005-05-01
Features: Based on the research and analysis of the distribution patterns of prime numbers, this book employs general mathematics (not advanced mathematics) and uses the Sieve of Eratosthenes (also known as the classical sieve method) to consider the starting point of the sieve. It identifies the distribution calculation patterns of twin primes, cousin primes, and triple primes, obtaining precise solutions, simplified solutions, and important conclusions. From RLn ≥ 1, Rpnk ≥ 1, and RLn1 ≥ 1, it follows that QL = RLn × m/2 ≥ m/2, Q2 ≥ QL/2 = RLn × m/4 ≥ m/4, and Q3 ≈ Rpnk × RLn1 × m/13 ≥ m/13. Therefore, it is concluded that limQL = ∞, Q2 = ∞, and Q3 = ∞. For the actual distribution of these prime arrays, they have all been meticulously checked using electronic computers. The main theoretical formulas for these calculations have also been computed on the computer, yielding preliminary verification. It can be summarized that the conclusions of the Goldbach conjecture and the twin prime conjecture are affirmative. The distribution data of prime arrays listed in the book may have certain reference value for future research in the mathematical community.