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Abstract
This paper presents 5 equations that generate all existing composite numbers. To find these equations, we divided all natural numbers in 6 groups and found the equations that generate all composite numbers in each one of these groups by means of simple mathematical reasoning. Two different ways to obtain prime numbers by iteration are provided. An iteration method to find twin prime numbers is also described.
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References
Pomerance, Carl (1982). "The Search for Prime Numbers". Scientific American. 247 (6): 136–147.
Mollin, Richard A. (2002). "A brief history of factoring and primality testing B. C. (before computers)". Mathematics Magazine. 75 (1): 18–29
Keyu, Y. A Review of the Development and Applications of Number Theory. 2019 J. Phys.: Conf. Ser. 1325
Chabert, Jean-Luc (2012). A History of Algorithms: From the Pebble to the Microchip.
Rosen, Kenneth H. (2000). "Theorem 9.20. Proth's Primality Test". Elementary Number Theory and Its Applications (4th ed.). Addison-Wesley. p. 342. ISBN 978-0-201-87073-2.
(2007). Primality Testing: An Overview. In: Number Theory. Birkhäuser Boston.
Bernstein, D. Distinguishing prime numbers from composite numbers: the state of the art in 2004. Mathematics Subject Classification (2004)
Granville, A. (1995). Unexpected Irregularities in the Distribution of Prime Numbers. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel.
Lamb, E. Peculiar pattern found in ‘random’ prime numbers. Nature (2016).
D. Goldston, J. Pintz and C. Yıldırım, Primes in tuples, I, preprint, available at www.arxiv.org.
Soundararajan K. SMALL GAPS BETWEEN PRIME NUMBERS: THE WORK OF GOLDSTON-PINTZ-YILDIRIM. available at www.arxiv.org.
Karatsuba A. A. A property of the set of prime numbers. Russian Math. Surveys 66:2 209-220.
Granville, A. Primes in intervals of bounded length, Bull. Amer. Math. Soc. 52 (2015), 171-222
Yitang Zhang, Bounded gaps between primes, Ann. of Math. (2) 179 (2014), no. 3, 1121–1174.
Robert J. Lemke Oliver, Kannan Soundararajan. “Unexpected biases in the distribution of consecutive primes”. Submitted Arxiv.org on 11 Mar 2016 (v1), last revised 30 May 2016.