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Fórmulas que generan números primos

  • Autores: Juan Fernández Sánchez, Rocío Sánchez Alcalde, Manuel Úbeda Flores Árbol académico
  • Localización: Epsilon: Revista de la Sociedad Andaluza de Educación Matemática "Thales", ISSN-e 2340-714X, ISSN 1131-9321, Nº 110, 2022, págs. 77-101
  • Idioma: español
  • Títulos paralelos:
    • Formulas that generate prime numbers
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  • Resumen
    • español

      Gracias a Euclides, es conocido desde hace más de dos mil años que existen infinitos números primos. Desde entonces, numerosas demostraciones lo han probado de diferentes maneras. Además, se han desarrollado fórmulas que permiten la generación de los números primos. El objetivo de este trabajo es hacer un compendio de las principales fórmulas generadoras de números primos, que permiten su obtención utilizando diferentes técnicas

    • English

      Thanks to Euclid, it has been known for more than two thousand years that there are infinite prime numbers. Since then, numerous proofs have proven this fact in different ways. In addition, formulas have been developed that allow the generation of prime numbers. The objective of this work is to make a compendium of the main formulas, which allow obtaining the prime numbers by using different techniques

  • Referencias bibliográficas
    • Alkauskas, G. y Dubickas, A. (2004). Prime and composite numbers as integer parts of powers. Acta Mathematica Hungarica, 105(3), 249–256.
    • Almansa, J. y Prieto, L. (1994). Nuevas fórmulas para el n-ésimo primo. Lecturas Matemáticas, 2(15), 227–231.
    • Ansari, A. R. (1951). On prime representing function. Ganita, 2, 81–82.
    • Assis, A. V. D. B. (2015). Formula to generate the sequence of prime numbers - explained. hal-01180298.
    • Atanassov, K. T. (2001). A new formula for the nth prime number. Comptes Rendus de l’Academie Bulgare des Sciences, 54(7), 5–6.
    • Atanassov, K. T. (2004). On a new formula for the nth prime number. Notes on Number Theory and Discrete Mathematics, 10(1), 24.
    • Atanassov, K.T. (2013). A formula for the nth prime number. Comptes Rendus de l’Academie Bulgare des Sciences, 66(4), 503–506.
    • Baker, R. C. y Harman, G. (1996). Primes of the form ⌊cp⌋. Mathematische Zeitschrift, 221, 73–81.
    • Bang, T. (1952). A function representing all prime numbers. Nordisk Matematisk Tidsskrift, 34, 117–118.
    • Chamizo, F., Raboso, D. y Ruiz-Cabello, S. (2011). On Rowland’s sequence. The Electronic Journal of Combinatorics, 18(2), paper 10, 10 pp.
    • Conway, J. H. (1983). FRACTRAN: a simple universal programming language for arithmetic. En T. M. Cover y B. Gopinath (Eds.). Open Problems...
    • Crandall, R. y Pomerance, C. (2005). Prime Numbers: A Computational Perspective, Second Edition. Springer, New York.
    • de Amo, E., Díaz Carrillo, M. y Fernández Sánchez, J. (2013). Demostraciones de la infinidad de los números primos. Épsilon - Revista de Educación...
    • Elliott, D. D. (1983). A prime-generating function. The Two-Year College Mathematics Journal, 14(1), 57.
    • Elsholtz, C. (2020). Unconditional prime-representing functions, following Mills. American Mathematical Monthly, 127(7), 639–642.
    • Erdős, P. (1932). Beweiseines Satzes von Tschebyschef. Acta Scientiarium Mathematicarum (Szeged), 5, 194–198.
    • Euler, L. (1741). Theorematum quorundam ad numerous primos spectantium demonstratio. Commentarii Academiae Scientiarum Petropolitanae, 8,...
    • Ernvall, R. (1975). A formula for the least prime greater than a given integer. Elemente der Mathematik, 30, 13–14.
    • Gandhi, J. M. (1971). Formulae for the nth prime. Proceedings of the Washington State University Conference on Number Theory, Washington State...
    • Gawlik, J. (1995). A function which distinguishes the prime numbers. Mathematics Today (Southend-on-sea) 33, 21.
    • Golomb, S.W. (1976). Formulas for the next prime. Pacific Journal of Mathematics, 63(2), 401–404.
    • Goodstein, R. L. y Wormell, C.P. (1967). Formulae for primes. Mathematical Gazette, 51(375), 35–38.
    • Guy, R. K. (1983). Conway’s prime producing machine. Mathematics Magazine, 56(1), 26–33.
    • Guy, R. K. (2004). Unsolved Problems in Number Theory. Third Edition. Springer, New York.
    • Hacks, J. (1893). Über einige für Primzahlen charakteristische Beziehungen. Acta Mathematica, 17(1), 205.
    • Hardy, G. H. y Wright, E. M. (1979). An Introduction to the Theory of Numbers. Fifth Edition. Oxford University Press, London.
    • Harris, V. C. (1969). A test for primality. Nordisk Matematisk Tidsskrift, 17(3), 82.
    • Isenkrahe, C. (1900). Ueber eine Lösung der Aufgabe, jede Primzahlals Function der vorhergehenden Primzahlen durch einen geschlossenen Ausdruck...
    • Jones, J. P. (1975). Formula for the nth prime number. Canadian Mathematical Bulletin, 18(3), 433–434.
    • Jones, J. P., Sato, D., Wada, H. y Wiens, D. (1976). Diophantine representation of the set of prime numbers. American Mathematical Monthly,...
    • Kaddoura, I. y Abdul-Nabi, S. (2012). On formula to compute primes and the nth prime. Applied Mathematics Science, 6(76), 3751–3757.
    • Keller, J. B. (2007). A recursion equation for prime numbers. arXiv:0711.3940 [math.NT].
    • Knopfmacher, J. (1979). Recursive formulae for prime numbers. Archiv der Mathematik (Basel), 33(1), 144–149.
    • Kuipers, L. (1950). Prime-representing functions. Indagationes Mathematicae, 12, 57–58.
    • Lagrange, J. L. (1771). Demonstration d’un théorème nouveau concernant les nombres premiers. Nouveaux Mémoires de l’Académie Royale des Sciences...
    • Lambert, J. H. (1771). Anlage zur Architectonic, oder Theorie des Einfachen und Ersten in der philosophischen und mathematischen Erkenntniss...
    • Matijasevič, Y. (1970). Enumerable sets are Diophantine (en ruso). Doklady Akademii Nauk SSSR, 191, 279–282. Traducido al inglés en Journal...
    • Matijasevič, Y. (1971). Diophantine representation for the set of prime numbers (en ruso). Doklady Akademii Nauk SSSR, 196, 770–773. Traducido...
    • Matijasevič, Y. (1977). Primes are non-negative values of a polynomial in 10 variables (en ruso). Zapiski Nauchnykh Seminarov LOMI, 68, 62–82.
    • Matomäki, K. (2010). Prime representing functions. Acta Mathematica Hungarica, 128(4), 307–314.
    • Mills, W. H. (1947). A prime-representing function. Bulletin of the American Mathematical Society, 53(6), 604.
    • Moser, L. (1950). A prime representing function. Mathematics Magazine, 23(3), 163–164.
    • Narkiewicz, W. (2000). The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer, New York.
    • Niven, I. (1951). Functions which represent prime numbers. Proceedings of the American Mathematical Society, 2, 753–755.
    • Ortega Costa, J. (1950). La formulación explícita de la función pi(x) de los números primos. Revista Matemática Hispanoamericana, 10(2), 72–76.
    • Papadimitriou, M. (1975). A recursion formula for the sequence of odd primes. The American Mathematical Monthly, 82(3), 289.
    • Raitzin, C. (1979). The exact count of the prime numbers that do not exceed a given upper bound. Rev. Ingr., 1, 37–43.
    • Regimbal, S. (1975). An explicit formula for the kth prime number. Mathematics Magazine, 48(4), 230–232.
    • Ribenboim, P. (2004). The Little Book of Bigger Primes. Second Edition. Springer, New York.
    • Riemann, B. (1859). Über die Anzahl der Primzahlen unter einer gegebenen Grösse. Monatsberichte der Berliner Akademie, 1859.
    • Rowland, E. S. (2008). A natural prime-generating recurrence. Journal of Integer Sequences, 11(2), article 08.2.8, 13 pp.
    • Ruiz, S. M. (2000). The general term of the prime number sequence and the Smarandache prime function. Smarandache Notions Journal, 11, 59–61.
    • Ruiz, S. M. y Sondow, J. (2014). Formulas for π(x) and the nth prime. International Journal of Mathematics and Computer Science, 9(2), 95–98.
    • Saouter, Y. (2017). A (doubly) elementary formula for prime numbers. Mathematical Gazette, 101(550), 93–95.
    • Scherk, H. F. (1833). Bemerkungen über die Bildung der Primzahlen aus einander. Journal für die Reine und Angewandte Mathematik, 10, 201–208.
    • Shevelev, V. (2009a). Generalizations of the Rowland theorem. arXiv:0911.3491v5 [math. NT].
    • Shevelev, V. (2009b). Infinite sets of generators of primes based on the Rowland idea and conjectures concerning twin primes. arXiv:0910.4676...
    • Sierpiński, W. (1952a). Sur une formule donnant tous les nombres premiers. Comptes Rendus de l’Académie des Sciences Paris, 235, 1078–1079.
    • Sierpiński, W. (1952b). Sur une propriété des nombres premiers. Bulletin de la Société Royale des Sciences de Liège, 21, 537–539.
    • Srinivasan, B. R. (1961). Formulae for the nth prime. Journal of the Indian Mathematical Society, 25, 33–39.
    • Sun, Z.-W. (2013). On functions taking only prime values. Journal of Number Theory, 133(8), 2794–2812.
    • Tee, G. J. (1972). Simple analytic expressions for primes and for prime pairs. The New Zealand Mathematics Magazine, 9, 32–44.
    • Teuffel, E. (1954). Eine Rekursions für Primzahlen. Jahresbericht der Deutschen Mathematiker-Vereinigung, 57(1), 34–36.
    • Tsangaris, P. G. (2004).Prime numbers and cyclotomy. Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae, 31, 3–10.
    • Tsangaris, P. G. (2007). Formulae for the kth prime number. Bulletin of the Greek Mathematical Society, 53, 147–149.
    • Tsangaris, P. G. y Jones, J. P. (1992). An old theorem on the cgd and its application to primes. Fibonacci Quarterly, 30(3), 194–198.
    • Tschebycheff, P. L. (1852a). Sur la fonction qui détermine la totalité des nombres premiers inférieurs à une limite donnée. Journal de Mathématiques,...
    • Tschebycheff, P. L. (1852b). Mémoire sur les nombres premiers. Journal de Mathématiques, 17, 366–390.
    • Vallata, L. y Omodeo, E. G. (2015). A Diophantine representation of Wolstenholme’s pseudoprimality. En D. Ancona, M. Maratea y V. Mascardi...
    • Vassilev-Missana, M. (2001). Three formulae for n-th prime and six for n-th term for twin primes. Notes on Number Theory and Discrete Mathematics,...
    • Vassilev-Missana, M. (2013). New explicit representations for the prime. Notes on Number Theory and Discrte Mathematics, 19(3), 24–27.
    • Willans, C. P. (1964). On formulae for the nth prime number. Mathematical Gazette, 84, 413–415.
    • Wright, E. M. (1951). A prime-representing function. The American Mathematical Monthly, 58, 616–618
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