Research ArticleOpen AccessGoogle Scholar indexed
The Proof of Goldbach’s Conjecture on Prime Numbers
Department of Mathematics and Statistics, York University, Toronto, Canada
- 1 Department of Mathematics and Statistics, York University, Toronto, Canada
Natural Science·Volume 11 (2019)·Pages 273–283·Published 11 September 2019·DOI10.4236/ns.2019.119029
Copy link · social · email
Abstract
Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2 n as well.
KeywordsProof of Goldbach’s ConjectureHidden Symmetry of PrimesMatching Primes and Composite IntegersArranging Odd Integers in FramesThe Existence and the Number of Goldbach Solutions
- Guiasu, S. (1995) Is There Any Regularity in the Distribution of Prime Numbers at the Beginning of the Sequence of Positive Integers? Mathematics Magazine, 68, 110-121. https://doi.org/10.1080/0025570X.1995.11996292
- Guiasu, S. (2018) A Hidden Stability in the Random Behaviour of the Consecutive Prime Numbers. Natural Science, 10, 385-392. https://doi.org/10.4236/ns.2018.1010036
- Guiasu, S. (2019) Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory. Natural Science, 11, 187-196. https://doi.org/10.4236/ns.2019.116019
- Mattmüller, M. and Lemmermeyer, F., Eds. (2015) Correspondence of Leonhard Euler with Christian Goldbach. Vol. 2, Birkhauser, Basel. https://doi.org/10.1007/978-3-0348-0893-4
- Olivera e Silva, T., Heorzog, S. and Pardi, S. (2014) Empirical Verification of the Even Goldbach’s Conjecture of Prime Gaps up to . Mathematics of Computation, 83, 2033-2060. https://doi.org/10.1090/S0025-5718-2013-02787-1
- Ramanujan, S. (1919) A Proof of Bertrand’s Postulate. Journal of Mathematical Society, 11, 181-182.