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Goldbach’s Conjecture and the 2-Way Sieve

Intro:

Mr. Hui Sai Chuen is an amateur mathematician born in May 1937 in the Canton province of China. After graduating with an engineering and construction degree, he proceeded to do research on architecture and material science before moving to Hong Kong in 1981. From there he enjoyed a successful career with various construction and interior design companies until his retirement in 1993. The ever-curious mathematician, Mr. Hui then dedicated his time to studying number theory, particularly Goldbach’s conjecture and its uses. He published his findings in several papers, two of which were the ‘2-Way Sieve’ and the ‘Double-Key Lock Cipher Theory’, both highly commended for its novelty in several national symposiums (the latter discovery was patented in China in 2004).

The 2-Way Sieve is a new sieve method created by Mr. Hui that can sieve odd prime number pairs. Although the formula has been verified by Professor Jong Ji of the South China Normal University and by the “Mathematics Journal” published by the Mathematics Research Institute of the Chinese Academy of Social Sciences in 2001, the theory is nonetheless somewhat novel, a new mathematical concept of a multifunctional sieve. Put simply, it can be explained as follows. For example:

Take any even number, w = 26 say.

We look at the set of its non-negative integers:

Forward Subset: S+ = 0, 1, 2, … , 24, 25, 26

Backward Subset: S- = 26, 25, 24, … , 2, 1, 0

S+= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

S-= 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

By combining the two subsets, we can see that the sum of any arbitrary pair of numbers is equal w = 26.

The prime factors of the subsets S+ and S- are:

√w = √26 = 5.099, which after rounding, the prime factors are 2, 3 and 5.

By sieving the numbers that can be divided exactly by 2, 3 and 5 in the subsets S+ and S-, we obtain the forward and reverse collection as follows:

S+= x 1 2 3 x 5 x 7 x x x 11 x 13 x x x 17 x 19 x x x 23 x x x

S-= x x x 23 x x x 19 x 17 x x x 13 x 11 x x x 7 x 5 x 3 2 1 x

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# Goldbach’s Conjecture and the 2-Way Sieve

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