Investigating the Primes
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The aim of this expository article is to introduce the reader to some of the fundamental milestones in the study of prime numbers across several centuries. Among the important developments in the study of prime numbers, we review the history of the prime number theorem, the Riemann zeta function (in relation to prime number theory), and some recent investigations into spacings between consecutive primes. We also present an important application of prime numbers in safe data transmission, namely the ‘RSA public key cryptosystem’.
KeywordsPrime numbers sieve methods Riemann zeta function cryptography
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- M H Weissman, Why Prime Numbers Still Fascinate Mathematicians, 2,300 Years Later, The Conversation, April 2, 2018. https://doi.org/theconversation.com/why-prime-numbers-still-fascinate-mathematicians-2-300-years-later-92484.Google Scholar
- B Riemann, Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse, Bernard Riemann’s Gesammelte Mathematische Werke Und Wissenschaftliche Nachlass, Zweite Auflage, pp.145–155, Teubner, Leipzig, 1892; reprinted, Dover, New York, 1953.Google Scholar
- A Granville, What is the Best Approach to Counting Primes? A century of Advancing Mathematics, Math. Assoc. America, pp.83–116,, Washington, DC, 2015.Google Scholar
- H M Edwards, Riemann’s Zeta Function, Reprint of the 1974 original [Academic Press, New York], Dover Publications, Inc., Mineola, NY, 2001.Google Scholar
- M R Murty, New Developments on the Twin Prime Problem and Generalizations, Hardy-Ramanujan Journal, Vol.37, pp.13–19, 2014.Google Scholar