Version 1
: Received: 19 August 2024 / Approved: 20 August 2024 / Online: 20 August 2024 (12:03:53 CEST)
Version 2
: Received: 5 September 2024 / Approved: 5 September 2024 / Online: 5 September 2024 (10:42:32 CEST)
Version 3
: Received: 25 October 2024 / Approved: 26 October 2024 / Online: 28 October 2024 (02:15:03 CET)
How to cite:
Szabó, P. On the Natural Numbers that cannot be Expressed as a Sum of Two Primes. Preprints2024, 2024081416. https://doi.org/10.20944/preprints202408.1416.v3
Szabó, P. On the Natural Numbers that cannot be Expressed as a Sum of Two Primes. Preprints 2024, 2024081416. https://doi.org/10.20944/preprints202408.1416.v3
Szabó, P. On the Natural Numbers that cannot be Expressed as a Sum of Two Primes. Preprints2024, 2024081416. https://doi.org/10.20944/preprints202408.1416.v3
APA Style
Szabó, P. (2024). On the Natural Numbers that cannot be Expressed as a Sum of Two Primes. Preprints. https://doi.org/10.20944/preprints202408.1416.v3
Chicago/Turabian Style
Szabó, P. 2024 "On the Natural Numbers that cannot be Expressed as a Sum of Two Primes" Preprints. https://doi.org/10.20944/preprints202408.1416.v3
Abstract
In the article, we define a sequence F: F(0) = 2, F(1) = 10, F(2) = 16, F(3) = 22, F(4) = 26, F(4) = 28, · · · , F(i) = F(i − 1) + l, where the number l ≤ 8 is defined by using prime numbers and matrix algebra. The sequence includes only even numbers and can be used to define a series of numbers F(i) + 1, the non-Goldbach sequence, that contains all numbers that cannot be written as the sum of two primes. The result is related to Goldbach’s conjecture. The famous Goldbach conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.
Keywords
circulant matrix; prime number; the Goldbach conjecture; the ternary Goldbach conjecture
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.