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A SHORT PROOF OF THE INFINITUDE OF PRIMES

Year 2025, Volume: 8 Issue: 2 , 1 - 2 , 01.06.2025
https://izlik.org/JA58HK45SG

Abstract

This paper aims to provide a short proof of the infinitude of prime numbers. Prime numbers, which form the foundation of number theory, have attracted the interest of mathematicians since ancient times. Many proofs have been made to show that there are infinitely many prime numbers. In this study, a new proof is presented using the method of proof by contradiction.

References

  • [1] Brocard H., L’Intermédiare des Math. 22, 1915, p. 253 [2] De la Vallée Poussin, C. J. (1896). Recherches analytiques sur la théorie des nombres premiers. Annales de la Société Scientifique de Bruxelles, 20, 183–256. [3] Hadamard, J. (1896). Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques. Bulletin de la Société Mathématique de France, 24, 199–220. [4] Heath, T. L. The Thirteen Books of Euclid’s Elements, vol. 2, University Press, Cambridge, 1908; 2nd ed. reprinted by Dover, New York, 1956. [5] Mesioye, A. & Ibharalu, F. T. (2024). A Fast Key Generation Algorithm for RSA Crypto System. [6] Mestrovic R. Euclid’s theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.–2012), 66 pages, preprint arXiv:1202.3670v2 [math.HO], 2012.

Year 2025, Volume: 8 Issue: 2 , 1 - 2 , 01.06.2025
https://izlik.org/JA58HK45SG

Abstract

References

  • [1] Brocard H., L’Intermédiare des Math. 22, 1915, p. 253 [2] De la Vallée Poussin, C. J. (1896). Recherches analytiques sur la théorie des nombres premiers. Annales de la Société Scientifique de Bruxelles, 20, 183–256. [3] Hadamard, J. (1896). Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques. Bulletin de la Société Mathématique de France, 24, 199–220. [4] Heath, T. L. The Thirteen Books of Euclid’s Elements, vol. 2, University Press, Cambridge, 1908; 2nd ed. reprinted by Dover, New York, 1956. [5] Mesioye, A. & Ibharalu, F. T. (2024). A Fast Key Generation Algorithm for RSA Crypto System. [6] Mestrovic R. Euclid’s theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.–2012), 66 pages, preprint arXiv:1202.3670v2 [math.HO], 2012.
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Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Research Article
Authors

Siyabend Turgut 0009-0003-0827-3716

Submission Date January 20, 2025
Acceptance Date April 4, 2025
Early Pub Date May 10, 2025
Publication Date June 1, 2025
IZ https://izlik.org/JA58HK45SG
Published in Issue Year 2025 Volume: 8 Issue: 2

Cite

APA Turgut, S. (2025). A SHORT PROOF OF THE INFINITUDE OF PRIMES. Journal of Advanced Mathematics and Mathematics Education, 8(2), 1-2. https://izlik.org/JA58HK45SG

Baş editör; Prof .Dr. Seyfullah Hızarcı