Keywords and phrases: prime numbers, primality test, recurrence formula.
Received: March 31, 2021; Accepted: April 23, 2021; Published: June 28, 2021
How to cite this article: Mario Mendoza Villalba and Danilo A. García Hernández, A recursive formula concerning the greatest prime number less than or equal to an odd number n, JP Journal of Algebra, Number Theory and Applications 51(1) (2021), 113-124. DOI: 10.17654/NT051010113
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] David C. Mapes, Fast method for computing the number of primes less than a given limit, Math. Comp. 17(82) (1963), 179-185. [2] D. R. Heath-Brown, The number of primes in a short interval, J. Reine Angew. Math. 389 (1988), 22-63. [3] D. R. Heath-Brown, Ueber die Formeln zur Berechnung der Anzahl der eine gegebene Grenze nicht übersteigenden Primzahlen, Krak. Ber. 28 (1995), 192-219. [4] D. R. Heath-Brown, On the exact number of primes below a given limit, Amer. Math. Monthly 53(9) (1946), 521-523. [5] Meissel, Ueber die Bestimmung der Primzahlenmenge innerhalb gegebener Grenzen, The Math. Ann. 2 (1870), 636-642 (in German). [6] Tom M. Apostol, Introduction to Analytic Number Theory, Springer Science and Business Media, 2013. [7] David M. Burton, Elementary Number Theory, Tata McGraw-Hill Education, 2006. [8] Ritu Patidar and Rupali Bhartiya, Modified RSA cryptosystem based on offline storage and prime number, IEEE International Conference on Computational Intelligence and Computing Research, 2013, pp. 1-6. [9] C. P. Willans, On Formulae for the nth Prime Number, Math. Gaz. 48 (1964), 413-415. [10] J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. [11] Godfrey Harold Hardy and Edward Maitland Wright, An Introduction to the Theory of Numbers, Oxford University Press, 1979. [12] Patrick Billingsley, Prime numbers and Brownian motion, Amer. Math. Monthly 80(10) (1973), 1099-1115. [13] J. Barkley Rosser and Lowell Schoenfeld, A function representing all prime numbers, Nordisk Mat. Tidskr 34 (1952), 117-118. [14] Gary L. Miller, Riemann’s hypothesis and tests for primality, J. Comput. System Sci. 13(3) (1976), 300-317. [15] Henri Cohen and Arjen Klaas Lenstra, Implementation of a new primality test, Math. Comp. 48(177) (1987), 103-121. [16] H. W. Lenstra, Jr, Miller’s primality test, Inform. Process. Lett. 8(2) (1979), 86-88. [17] Ø. J. Rødseth, A note on primality tests for BIT 34(3) (1994), 451-454.
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