A SHORT PROOF OF THE INFINITUDE OF PRIMES

Yıl 2025, Cilt: 8 Sayı: 2, 1 - 2, 01.06.2025

Siyabend Turgut

Öz

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.

Anahtar Kelimeler

prime numbers, infinitude of primes, number theory

Kaynakça

• [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.