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Article Content:-
Abstract
The paper uses the structure and math of Prime Generator Theory to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.
References:-
References
The Use of Prime Generators to Implement Fast Twin Primes Sieve of Zakiya (SoZ), Applications to Number Theory, and Implications to the Riemann Hypothesis, Jabari Zakiya, 2019. - https://www.academia.edu/37952623The_Use_of_Prime_Generators_to_ Implement_Fast_Twin_Primes_Sieve_of_Zakiya_SoZ_Applications_to_Number_Theory_ and_Implications_for_the_Riemann_Hypotheses
The Segmented Sieve of Zakiya (SSoZ), Jabari Zakiya, 2014. - https://www.academia.edu/ 7583194/The_Segmented_Sieve_of_Zakiya_SSoZ
Twin Primes Segmented Sieve of Zakiya (SSoZ) Explained, Jabari Zakiya, J Curr Trends Comp Sci Res 2(2), 119-147, 2023. - https://www.opastpublishers.com/open-access-articles/ twin-primes-segmented-sieve-of-zakiya-ssoz-explained.pdf
k-tuples page - https://en.wikipedia.org/wiki/Prime_k-tuple
Twin Prime - https://en.wikipedia.org/wiki/Twin_prime
Polignac’s Conjecture - https://en.wikipedia.org/wiki/Polignac%27s_conjecture
PRIMES-UTILS HANDBOOK, Jabari Zakiya, 2016. - https://www.academia.edu/19786419/ PRIMES_UTILS_HANDBOOK
(Simplest) Proof of Twin Primes and Polignac’s Conjectures (video), Jabari Zakiya, 2021. https://www.youtube.com/watch?v=HCUiPknHtfY
Jumping Champions, Andrew Odlyzko,Micheal Rubinstein, Mark Wolf, Experimental Mathematics, 8(2), 107-118, 1999. - https://projecteuclid.org/journals/ experimental-mathematics/volume-8/issue-2/Jumping-champions/em/1047477055.full