A Proof on the Conjecture of Twin Primes

Received: 15 July 2019     Accepted: 27 July 2019     Published: 20 September 2019
Abstract

Although the mathematicians all over the world offered hard explorations of more than one hundred years, the proof of using pure mathematical theories on the conjecture of twin primes has not born in the world. This paper is trying to apply computer program to prove that corresponding to infinite primes p, there are infinite p+2 primes. As a mathematical proof, the paper uses the concept of mapping to connect the computer program and the pure mathematical theory. With the requirement of a mathematical proof, in accord with the restriction of the integer of which the computer allows to take, an assumption is suggested, and on the basis of it, using the program of C language the paper presents, or regarding the C program as the mapping from infinite p primes to infinite p+2 primes, the paper proves that corresponding to infinite primes p, there are infinite p+2 primes; namely, the conjecture of twin primes is true.

Keywords

Conjecture of Twin Primes, Mapping, Assumption, Program of C Language

References
 [1] Chen Jing-Run. On some problems in prime number theory [C]. Paris: Seminaire de Theorie des Nombnes, 1979-1980: 167-170. [2] Brian Conrey and Jonathan P. Keating. Pair Correlations and Twin Primes Revisited [J]. Proc. Math. Phys. Eng. Sci., 2016, 472 (2194): 20160548. [3] Zhou Zuo-Ling. A Proof of the Conjecture on the Twin Primes [C]. AIP Conference Proceedings, 2016, 1738 (1): 260002. [4] Hayat Rezgui. Conjecture of Twin Primes (Still Unsolved Problem in Number Theory). An Expository Essay [J]. Surveys in Mathematics and Its Applications, 2017, 12: 229-252. [5] Renato Betti. The Twin Primes Conjecture and Other Curiosities Regarding Prime Numbers [J]. Lettera Matematica, 2017, 5 (4): 297-303. [6] T. J. Hoskins. Proofs of the Twin Primes and Goldbach Conjectures [J]. arXiv. 1901.09668v7 [Math. GM] (e-print), 2019, 7: 1-33. [7] Andri Lopez. Twin Primes Conjecture and Two Problem More [J]. International Journal of Mathematics and Computation, 2018, 29 (4): 63-66. 107 (1): 55-56. [8] Maria Suzuki. Alternative Formulations of the Twin Prime Problem [J]. The American Mathematical Monthly, 2000, 107 (1): 55-56. [9] Juan G. Orozco. An Algorithmic Proof of the Twin Primes Conjecture and the Goldbach Conjecture, viXra.org > number theory > viXra. 1701.0618 [v4], 2018-01-30. [10] Dieter Sengschmitt. Proof on the Twin Prime Conjecture [J]. viXra.org, Number Theory, viXra: 1710.0042, 2017-10-03. [11] M. Ram Murty and Akshaa Vatwani. Twin Primes and the Prity Problem [J]. Journal of Number Teory, 2017, 180: 643-659. [12] Stephan Ramon Garcia, Elvis Kahoro and Florian Luca. Primitive Root Bias for Twin Primes [J]. Experimental Mathematics, 2019, 28 (2): 151-160. [13] Ramon Ruiz. About the Twin Primes Conjecture [J]. viXra.org, Number Theory, viXra: 1709.0417 [v1], 2017-09-28. [14] The Mathematical Society of Japan. The Dictionary of Mathematical Encyclopedias (Translation in Chinese) [M]. Beijing: Science Press, 1984: 42-45. [15] Guy Richard. Unsolved Problems in Number Theory Volume I (M). New York: Springer-Verlag, New York Inc., 1981: 13.
• APA Style

Zhang Yue. (2019). A Proof on the Conjecture of Twin Primes. International Journal of Applied Mathematics and Theoretical Physics, 5(3), 82-84. https://doi.org/10.11648/j.ijamtp.20190503.15

ACS Style

Zhang Yue. A Proof on the Conjecture of Twin Primes. Int. J. Appl. Math. Theor. Phys. 2019, 5(3), 82-84. doi: 10.11648/j.ijamtp.20190503.15

AMA Style

Zhang Yue. A Proof on the Conjecture of Twin Primes. Int J Appl Math Theor Phys. 2019;5(3):82-84. doi: 10.11648/j.ijamtp.20190503.15

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title = {A Proof on the Conjecture of Twin Primes},
journal = {International Journal of Applied Mathematics and Theoretical Physics},
volume = {5},
number = {3},
pages = {82-84},
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abstract = {Although the mathematicians all over the world offered hard explorations of more than one hundred years, the proof of using pure mathematical theories on the conjecture of twin primes has not born in the world. This paper is trying to apply computer program to prove that corresponding to infinite primes p, there are infinite p+2 primes. As a mathematical proof, the paper uses the concept of mapping to connect the computer program and the pure mathematical theory. With the requirement of a mathematical proof, in accord with the restriction of the integer of which the computer allows to take, an assumption is suggested, and on the basis of it, using the program of C language the paper presents, or regarding the C program as the mapping from infinite p primes to infinite p+2 primes, the paper proves that corresponding to infinite primes p, there are infinite p+2 primes; namely, the conjecture of twin primes is true.},
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Author Information
• Department of Physics, Hunan Normal University, Changsha, China

• Sections