Author(s)

Yichun Xiao ¹

Affiliation(s)

¹ Derun Pharmacy, Dezhou, Shandong, 251507, China

Corresponding Author

Yichun Xiao

ABSTRACT

Using a 0 to N₃ segment X_B number axis to move two number axis units to the right and then overlap with a 0 to N₃ segment X_A number axis in the same direction, it's found that the overlapping number axis points of the two prime numbers are a set of twin prime numbers, and the law of twin prime numbers smaller than N₃. Then, using the two X_A number axes of the same length with them to overlapped in the opposite direction, it is found that the overlapping axis points of the twin primes are P ( 1,1 ), which is the twin primes of N₃, which proves that N₃ can also be expressed as the sum of several groups of two primes. Comparing the two overlapping number axes, it is found that the X_A\X_A′ overlapping number axes are symmetrical,  and it is found that prime numbers that  make 6Pa  exactly divide (N₃-2Pa) or 6Pb exactly divide ((N₃+2P_b) can also increase the table method number of P(1,1) prime pairs of N₃, which proves that the number of P ( 1,1 ) primes of N₃ to the table group is about equal to or more than half of the number of twin primes which is smaller than N₃.

KEYWORDS

An Even Number Which Minus 2 Can Be Exactly Divided By 6, P(1, 1) Prime Pairs, Twin Prime Number, Overlapping Number Axes

CITE THIS PAPER

Yichun Xiao, Research on an Even Number Which Minus 2 Can be Exactly Divided by 6 Can be Expressed as the Sum of Several Sets of Two Prime Numbers. Transactions on Computational and Applied Mathematics (2024) Vol. 4: 86-94. DOI: http://dx.doi.org/10.23977/tracam.2024.040112.

REFERENCES

[1] Xiao Yichun. An even Number Divisible by 6 could be Expressed as the Sum of Several Groups of Two Prime Numbers. International Journal of Educational Curriculum Management and Research (2023), Vol. 4, Issue 3: 49-60. 
[2] Xiao Yichun. Classification of Prime Number. Digital Users. 2022 (5): 140.

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