Author(s)

Yichun Xiao ¹

Affiliation(s)

¹ Derun Pharmacy, Dezhou, Shandong, 251507, China

Corresponding Author

Yichun Xiao

ABSTRACT

The X_B number axis of a 0 to N₁ segment is shifted to the right by two number axis units and then overlapped in the same direction with the X_A number axis of a 0 to N₁ segment. The overlapped number axis points of the two primes number are a set of twin primes and the law of twin primes smaller than N₁ is found. Then, the two X_B number axes with the same length as them overlap in the opposite direction, and it is found that the overlapping number axis points of the two primes are the P (1,1) prime pairs of N₁, which proves that N₁ 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_B\X_B′ overlapping number axes are symmetrical, and it is found that prime numbers that  make 6P_a exactly divide (N₁+2P_a) or 6P_b  exactly divide (N₁-2P_b) can also increase the table method number of P(1,1) prime pairs of N₁, which proves that the number of P (1,1) primes of N₁ to the table group is about equal to or more than half of the number of twin primes smaller than N₁.

KEYWORDS

An Even Number Which Plus 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 Plus 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: 78-85. DOI: http://dx.doi.org/10.23977/tracam.2024.040111.

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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