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    Title: An Approximation Solution for the Twin Prime Conjecture
    Authors: Yensen Ni;Paoyu Huang;Yuhsin Chen
    Keywords: Twin Primes;Number Theory;Prime Number;Incremental Range
    Date: 2019-03
    Issue Date: 2018-10-16 12:10:56 (UTC+8)
    Publisher: 淡江大學
    Abstract: Journal of Applied Science and Engineering: In this study, we investigate the existence of numerous twin prime pairs according to the prime number inferred by the sieve of Eratosthenes. Given a number M=(6n+5)^2, at least three twin prime pairs can be found from the incremental range, which is increased from (6n+5)^2 to [6(n+1)+5]^2 for n=0 to infinite. Thus, we might be able to prove the twin prime conjecture proposed by de Polignac in 1849, that is, several prime numbers p exist for each natural number k by denoting p+2k as the prime number when k=1. Instead of twin prime pairs occurring irregularly, we infer that the twin prime conjecture solution might solved by satisfying two conditions: (1) eliminating the nontwin prime pairs in associated twin prime pairs would be regular, and (2) the incremental range from (6n+5)^2 to [6(n+1)+5]^2 for n=0 to ∞ would be regular. These conditions may not have been considered in previous studies that explored the question on whether numerous twin prime pairs exist, which has been one of the open questions in number theory for more than a century.
    Relation: Journal of Applied Science and Engineering 22(1), p.19-28
    DOI: 10.6180/jase.201903_22(1).0003
    Appears in Collections:[Department of Management Sciences] Journal Article

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