Պարզ թիվ (Armenian Wikipedia)

Analysis of information sources in references of the Wikipedia article "Պարզ թիվ" in Armenian language version.

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mathscinet.ams.org

Ziegler, Günter M. (2004). «The great prime number record races». Notices of the American Mathematical Society. 51 (4): 414–416. MR 2039814.
Sierpiński, Wacław (1964). A Selection of Problems in the Theory of Numbers. New York: Macmillan. էջ 40. MR 0170843.
Nathanson, Melvyn B. (2000). «Notations and Conventions». Elementary Methods in Number Theory. Graduate Texts in Mathematics. Vol. 195. Springer. ISBN 978-0-387-22738-2. MR 1732941.
Bruins, Evert Marie, review in Mathematical Reviews of Gillings, R.J. (1974). «The recto of the Rhind Mathematical Papyrus. How did the ancient Egyptian scribe prepare it?». Archive for History of Exact Sciences. 12 (4): 291–298. doi:10.1007/BF01307175. MR 0497458. S2CID 121046003.
Mollin, Richard A. (2002). «A brief history of factoring and primality testing B. C. (before computers)». Mathematics Magazine. 75 (1): 18–29. doi:10.2307/3219180. JSTOR 3219180. MR 2107288.
Apostol, Tom M. (2000). «A centennial history of the prime number theorem». In Bambah, R.P.; Dumir, V.C.; Hans-Gill, R.J. (eds.). Number Theory. Trends in Mathematics. Basel: Birkhäuser. էջեր 1–14. MR 1764793.
Apostol, Tom M. (1976). «7. Dirichlet's Theorem on Primes in Arithmetical Progressions». Introduction to Analytic Number Theory. New York; Heidelberg: Springer-Verlag. էջեր 146–156. MR 0434929.
Katz, Shaul (2004). «Berlin roots – Zionist incarnation: the ethos of pure mathematics and the beginnings of the Einstein Institute of Mathematics at the Hebrew University of Jerusalem». Science in Context. 17 (1–2): 199–234. doi:10.1017/S0269889704000092. MR 2089305. S2CID 145575536.
Caldwell, Chris K.; Reddick, Angela; Xiong, Yeng; Keller, Wilfrid (2012). «The history of the primality of one: a selection of sources». Journal of Integer Sequences. 15 (9): Article 12.9.8. MR 3005523. For a selection of quotes from and about the ancient Greek positions on the status of 1 and 2, see in particular pp. 3–4. For the Islamic mathematicians, see p. 6.
Caldwell, Chris K.; Xiong, Yeng (2012). «What is the smallest prime?» (PDF). Journal of Integer Sequences. 15 (9): Article 12.9.7. MR 3005530.
Riesel, Hans (1994). Prime Numbers and Computer Methods for Factorization (2nd ed.). Basel, Switzerland: Birkhäuser. էջ 36. doi:10.1007/978-1-4612-0251-6. ISBN 978-0-8176-3743-9. MR 1292250.
Conway, John Horton; Guy, Richard K. (1996). The Book of Numbers. New York: Copernicus. էջեր 129–130. doi:10.1007/978-1-4612-4072-3. ISBN 978-0-387-97993-9. MR 1411676.
Furstenberg, Harry (1955). «On the infinitude of primes». American Mathematical Monthly. 62 (5): 353. doi:10.2307/2307043. JSTOR 2307043. MR 0068566.
Oliveira e Silva, Tomás; Herzog, Siegfried; Pardi, Silvio (2014). «Empirical verification of the even Goldbach conjecture and computation of prime gaps up to $4\cdot 10^{18}$ ». Mathematics of Computation. 83 (288): 2033–2060. doi:10.1090/S0025-5718-2013-02787-1. MR 3194140.
Ramaré, Olivier (1995). «On Šnirel'man's constant». Annali della Scuola Normale Superiore di Pisa. 22 (4): 645–706. MR 1375315. Արխիվացված է օրիգինալից 2022 թ․ փետրվարի 9-ին. Վերցված է 2018 թ․ հունվարի 23-ին.
Rassias, Michael Th. (2017). Goldbach's Problem: Selected Topics. Cham: Springer. էջ vii. doi:10.1007/978-3-319-57914-6. ISBN 978-3-319-57912-2. MR 3674356.

archive.org

Gardiner, Anthony (1997). The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965–1996. Oxford University Press. էջ 26. ISBN 978-0-19-850105-3.
Adler, Irving (1960). The Giant Golden Book of Mathematics: Exploring the World of Numbers and Space. Golden Press. էջ 16. OCLC 6975809.
Leff, Lawrence S. (2000). Math Workbook for the SAT I. Barron's Educational Series. էջ 360. ISBN 978-0-7641-0768-9.
Dudley, Underwood (1978). «Section 2: Unique factorization». Elementary number theory (2nd ed.). W.H. Freeman and Co. էջ 10. ISBN 978-0-7167-0076-0.
Sierpiński, Wacław (1964). A Selection of Problems in the Theory of Numbers. New York: Macmillan. էջ 40. MR 0170843.
Pomerance, Carl (1982 թ․ դեկտեմբեր). «The Search for Prime Numbers». Scientific American. 247 (6): 136–147. Bibcode:1982SciAm.247f.136P. doi:10.1038/scientificamerican1282-136. JSTOR 24966751.
Mollin, Richard A. (2002). «A brief history of factoring and primality testing B. C. (before computers)». Mathematics Magazine. 75 (1): 18–29. doi:10.2307/3219180. JSTOR 3219180. MR 2107288.
Conway, John Horton; Guy, Richard K. (1996). The Book of Numbers. New York: Copernicus. էջեր 129–130. doi:10.1007/978-1-4612-4072-3. ISBN 978-0-387-97993-9. MR 1411676.
du Sautoy, Marcus (2003). The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. Harper Collins. էջ 23. ISBN 978-0-06-093558-0.
Rotman, Joseph J. (2000). A First Course in Abstract Algebra (2nd ed.). Prentice Hall. Problem 1.40, p. 56. ISBN 978-0-13-011584-3.
Furstenberg, Harry (1955). «On the infinitude of primes». American Mathematical Monthly. 62 (5): 353. doi:10.2307/2307043. JSTOR 2307043. MR 0068566.
Mackinnon, Nick (1987 թ․ հունիս). «Prime number formulae». The Mathematical Gazette. 71 (456): 113–114. doi:10.2307/3616496. JSTOR 3616496. S2CID 171537609.
Wright, E.M. (1951). «A prime-representing function». American Mathematical Monthly. 58 (9): 616–618. doi:10.2307/2306356. JSTOR 2306356.
Green, Ben; Tao, Terence (2008). «The primes contain arbitrarily long arithmetic progressions». Annals of Mathematics. 167 (2): 481–547. arXiv:math.NT/0404188. doi:10.4007/annals.2008.167.481. S2CID 1883951.

arxiv.org

Green, Ben; Tao, Terence (2008). «The primes contain arbitrarily long arithmetic progressions». Annals of Mathematics. 167 (2): 481–547. arXiv:math.NT/0404188. doi:10.4007/annals.2008.167.481. S2CID 1883951.

books.google.com

Henderson, Anne (2014). Dyslexia, Dyscalculia and Mathematics: A practical guide (2nd ed.). Routledge. էջ 62. ISBN 978-1-136-63662-2.
Dudley, Underwood (1978). «Section 2: Unique factorization». Elementary number theory (2nd ed.). W.H. Freeman and Co. էջ 10. ISBN 978-0-7167-0076-0.
Sierpiński, Wacław (1988). Elementary Theory of Numbers. North-Holland Mathematical Library. Vol. 31 (2nd ed.). Elsevier. էջ 113. ISBN 978-0-08-096019-7.
Stillwell, John (1997). Numbers and Geometry. Undergraduate Texts in Mathematics. Springer. էջ 9. ISBN 978-0-387-98289-2.
Nathanson, Melvyn B. (2000). «Notations and Conventions». Elementary Methods in Number Theory. Graduate Texts in Mathematics. Vol. 195. Springer. ISBN 978-0-387-22738-2. MR 1732941.
Faticoni, Theodore G. (2012). The Mathematics of Infinity: A Guide to Great Ideas. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Vol. 111 (2nd ed.). John Wiley & Sons. էջ 44. ISBN 978-1-118-24382-4.
Stillwell, John (2010). Mathematics and Its History. Undergraduate Texts in Mathematics (3rd ed.). Springer. էջ 40. ISBN 978-1-4419-6052-8.
Sandifer 2007, 8. Fermat's Little Theorem (November 2003), p. 45
Sandifer, C. Edward (2014). How Euler Did Even More. Mathematical Association of America. էջ 42. ISBN 978-0-88385-584-3.
Koshy, Thomas (2002). Elementary Number Theory with Applications. Academic Press. էջ 369. ISBN 978-0-12-421171-1.
Yuan, Wang (2002). Goldbach Conjecture. Series In Pure Mathematics. Vol. 4 (2nd ed.). World Scientific. էջ 21. ISBN 978-981-4487-52-8.
Narkiewicz, Wladyslaw (2000). «1.2 Sum of Reciprocals of Primes». The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer Monographs in Mathematics. Springer. էջ 11. ISBN 978-3-540-66289-1.
Apostol, Tom M. (2000). «A centennial history of the prime number theorem». In Bambah, R.P.; Dumir, V.C.; Hans-Gill, R.J. (eds.). Number Theory. Trends in Mathematics. Basel: Birkhäuser. էջեր 1–14. MR 1764793.
Apostol, Tom M. (1976). «7. Dirichlet's Theorem on Primes in Arithmetical Progressions». Introduction to Analytic Number Theory. New York; Heidelberg: Springer-Verlag. էջեր 146–156. MR 0434929.
Chabert, Jean-Luc (2012). A History of Algorithms: From the Pebble to the Microchip. Springer. էջ 261. ISBN 978-3-642-18192-4.
Cooper, S. Barry; Hodges, Andrew (2016). The Once and Future Turing. Cambridge University Press. էջեր 37–38. ISBN 978-1-107-01083-3.
Beiler, Albert H. (1999) [1966]. Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover. էջ 2. ISBN 978-0-486-21096-4. OCLC 444171535.
Kraft, James S.; Washington, Lawrence C. (2014). Elementary Number Theory. Textbooks in mathematics. CRC Press. էջ 7. ISBN 978-1-4987-0269-0.
Bauer, Craig P. (2013). Secret History: The Story of Cryptology. Discrete Mathematics and Its Applications. CRC Press. էջ 468. ISBN 978-1-4665-6186-1.
Klee, Victor; Wagon, Stan (1991). Old and New Unsolved Problems in Plane Geometry and Number Theory. Dolciani mathematical expositions. Vol. 11. Cambridge University Press. էջ 224. ISBN 978-0-88385-315-3.
Tarán, Leonardo (1981). Speusippus of Athens: A Critical Study With a Collection of the Related Texts and Commentary. Philosophia Antiqua : A Series of Monographs on Ancient Philosophy. Vol. 39. Brill. էջեր 35–38. ISBN 978-90-04-06505-5.
Riesel, Hans (1994). Prime Numbers and Computer Methods for Factorization (2nd ed.). Basel, Switzerland: Birkhäuser. էջ 36. doi:10.1007/978-1-4612-0251-6. ISBN 978-0-8176-3743-9. MR 1292250.
For the totient, see Sierpiński 1988, p. 245. For the sum of divisors, see Sandifer, C. Edward (2007). How Euler Did It. MAA Spectrum. Mathematical Association of America. էջ 59. ISBN 978-0-88385-563-8.
Smith, Karl J. (2011). The Nature of Mathematics (12th ed.). Cengage Learning. էջ 188. ISBN 978-0-538-73758-6.
Dudley 1978, Section 2, Theorem 2, p. 16; Neale, Vicky (2017). Closing the Gap: The Quest to Understand Prime Numbers. Oxford University Press. p. 107. ISBN 978-0-19-109243-5.
Dudley 1978, Section 2, Lemma 5, p. 15; Higgins, Peter M. (1998). Mathematics for the Curious. Oxford University Press. էջեր 77–78. ISBN 978-0-19-150050-3.
Ribenboim, Paulo (2004). The little book of bigger primes. Berlin; New York: Springer-Verlag. էջ 4. ISBN 978-0-387-20169-6.
Matiyasevich, Yuri V. (1999). «Formulas for prime numbers». In Tabachnikov, Serge (ed.). Kvant Selecta: Algebra and Analysis. Vol. II. American Mathematical Society. էջեր 13–24. ISBN 978-0-8218-1915-9.
Guy 2013, p. vii.
Guy 2013, C1 Goldbach's conjecture, pp. 105–107.
Tao 2009, 3.1 Structure and randomness in the prime numbers, pp. 239–247. See especially p. 239.
Rassias, Michael Th. (2017). Goldbach's Problem: Selected Topics. Cham: Springer. էջ vii. doi:10.1007/978-3-319-57914-6. ISBN 978-3-319-57912-2. MR 3674356.
Koshy 2002, Theorem 2.14, p. 109. Riesel 1994 gives a similar argument using the primorial in place of the factorial.
Riesel 1994, "Large gaps between consecutive primes", pp. 78–79.
Sandifer 2007, Chapter 35, Estimating the Basel problem, pp. 205–208.
Ogilvy, C.S.; Anderson, J.T. (1988). Excursions in Number Theory. Dover Publications Inc. էջեր 29–35. ISBN 978-0-486-25778-5.
Miller, Steven J.; Takloo-Bighash, Ramin (2006). An Invitation to Modern Number Theory. Princeton University Press. էջեր 43–44. ISBN 978-0-691-12060-7.
Crandall & Pomerance 2005, p. 6.
Crandall & Pomerance 2005, Section 3.7, Counting primes, pp. 152–162.
Crandall & Pomerance 2005, p. 10.
du Sautoy, Marcus (2011). «What are the odds that your telephone number is prime?». The Number Mysteries: A Mathematical Odyssey through Everyday Life. St. Martin's Press. էջեր 50–52. ISBN 978-0-230-12028-0.
Gelfand, I.M.; Shen, Alexander (2003). Algebra. Springer. էջ 37. ISBN 978-0-8176-3677-7.
Mollin, Richard A. (1997). Fundamental Number Theory with Applications. Discrete Mathematics and Its Applications. CRC Press. էջ 76. ISBN 978-0-8493-3987-5.
Crandall & Pomerance 2005, Theorem 1.1.5, p. 12.

clarku.edu

aleph0.clarku.edu

Euclid's Elements, Book IX, Proposition 20. See David Joyce's English translation of Euclid's proof or Williamson, James (1782). The Elements of Euclid, With Dissertations. Oxford: Օքսֆորդի համալսարանի հրատարակչություն. էջ 63. OCLC 642232959.

dartmouth.edu

math.dartmouth.edu

Letter in Latin from Goldbach to Euler, July 1730.

doi.org

Bruins, Evert Marie, review in Mathematical Reviews of Gillings, R.J. (1974). «The recto of the Rhind Mathematical Papyrus. How did the ancient Egyptian scribe prepare it?». Archive for History of Exact Sciences. 12 (4): 291–298. doi:10.1007/BF01307175. MR 0497458. S2CID 121046003.
Pomerance, Carl (1982 թ․ դեկտեմբեր). «The Search for Prime Numbers». Scientific American. 247 (6): 136–147. Bibcode:1982SciAm.247f.136P. doi:10.1038/scientificamerican1282-136. JSTOR 24966751.
Mollin, Richard A. (2002). «A brief history of factoring and primality testing B. C. (before computers)». Mathematics Magazine. 75 (1): 18–29. doi:10.2307/3219180. JSTOR 3219180. MR 2107288.
Katz, Shaul (2004). «Berlin roots – Zionist incarnation: the ethos of pure mathematics and the beginnings of the Einstein Institute of Mathematics at the Hebrew University of Jerusalem». Science in Context. 17 (1–2): 199–234. doi:10.1017/S0269889704000092. MR 2089305. S2CID 145575536.
Riesel, Hans (1994). Prime Numbers and Computer Methods for Factorization (2nd ed.). Basel, Switzerland: Birkhäuser. էջ 36. doi:10.1007/978-1-4612-0251-6. ISBN 978-0-8176-3743-9. MR 1292250.
Conway, John Horton; Guy, Richard K. (1996). The Book of Numbers. New York: Copernicus. էջեր 129–130. doi:10.1007/978-1-4612-4072-3. ISBN 978-0-387-97993-9. MR 1411676.
Furstenberg, Harry (1955). «On the infinitude of primes». American Mathematical Monthly. 62 (5): 353. doi:10.2307/2307043. JSTOR 2307043. MR 0068566.
Mackinnon, Nick (1987 թ․ հունիս). «Prime number formulae». The Mathematical Gazette. 71 (456): 113–114. doi:10.2307/3616496. JSTOR 3616496. S2CID 171537609.
Wright, E.M. (1951). «A prime-representing function». American Mathematical Monthly. 58 (9): 616–618. doi:10.2307/2306356. JSTOR 2306356.
Oliveira e Silva, Tomás; Herzog, Siegfried; Pardi, Silvio (2014). «Empirical verification of the even Goldbach conjecture and computation of prime gaps up to $4\cdot 10^{18}$ ». Mathematics of Computation. 83 (288): 2033–2060. doi:10.1090/S0025-5718-2013-02787-1. MR 3194140.
Rassias, Michael Th. (2017). Goldbach's Problem: Selected Topics. Cham: Springer. էջ vii. doi:10.1007/978-3-319-57914-6. ISBN 978-3-319-57912-2. MR 3674356.
Chan, Joel (1996 թ․ փետրվար). «Prime time!». Math Horizons. 3 (3): 23–25. doi:10.1080/10724117.1996.11974965. JSTOR 25678057. Note that Chan lists Legendre's conjecture as "Sierpinski's Postulate".
Green, Ben; Tao, Terence (2008). «The primes contain arbitrarily long arithmetic progressions». Annals of Mathematics. 167 (2): 481–547. arXiv:math.NT/0404188. doi:10.4007/annals.2008.167.481. S2CID 1883951.

harvard.edu

ui.adsabs.harvard.edu

Pomerance, Carl (1982 թ․ դեկտեմբեր). «The Search for Prime Numbers». Scientific American. 247 (6): 136–147. Bibcode:1982SciAm.247f.136P. doi:10.1038/scientificamerican1282-136. JSTOR 24966751.

hathitrust.org

babel.hathitrust.org

Euclid's Elements, Book IX, Proposition 20. See David Joyce's English translation of Euclid's proof or Williamson, James (1782). The Elements of Euclid, With Dissertations. Oxford: Օքսֆորդի համալսարանի հրատարակչություն. էջ 63. OCLC 642232959.

jstor.org

Pomerance, Carl (1982 թ․ դեկտեմբեր). «The Search for Prime Numbers». Scientific American. 247 (6): 136–147. Bibcode:1982SciAm.247f.136P. doi:10.1038/scientificamerican1282-136. JSTOR 24966751.
Mollin, Richard A. (2002). «A brief history of factoring and primality testing B. C. (before computers)». Mathematics Magazine. 75 (1): 18–29. doi:10.2307/3219180. JSTOR 3219180. MR 2107288.
Furstenberg, Harry (1955). «On the infinitude of primes». American Mathematical Monthly. 62 (5): 353. doi:10.2307/2307043. JSTOR 2307043. MR 0068566.
Mackinnon, Nick (1987 թ․ հունիս). «Prime number formulae». The Mathematical Gazette. 71 (456): 113–114. doi:10.2307/3616496. JSTOR 3616496. S2CID 171537609.
Wright, E.M. (1951). «A prime-representing function». American Mathematical Monthly. 58 (9): 616–618. doi:10.2307/2306356. JSTOR 2306356.
Chan, Joel (1996 թ․ փետրվար). «Prime time!». Math Horizons. 3 (3): 23–25. doi:10.1080/10724117.1996.11974965. JSTOR 25678057. Note that Chan lists Legendre's conjecture as "Sierpinski's Postulate".

mathdoc.fr

sites.mathdoc.fr

Tchebychev, P. (1852). «Mémoire sur les nombres premiers» (PDF). Journal de mathématiques pures et appliquées. Série 1 (ֆրանսերեն): 366–390.. (Proof of the postulate: 371–382). Also see Mémoires de l'Académie Impériale des Sciences de St. Pétersbourg, vol. 7, pp. 15–33, 1854

mersenne.org

«GIMPS Project Discovers Largest Known Prime Number: 2^82,589,933-1». Mersenne Research, Inc. 2018 թ․ դեկտեմբերի 21. Վերցված է 2018 թ․ դեկտեմբերի 21-ին.

numdam.org

Ramaré, Olivier (1995). «On Šnirel'man's constant». Annali della Scuola Normale Superiore di Pisa. 22 (4): 645–706. MR 1375315. Արխիվացված է օրիգինալից 2022 թ․ փետրվարի 9-ին. Վերցված է 2018 թ․ հունվարի 23-ին.

oeis.org

Sloane, N. J. A. (ed.). «Sequence A100964 (Smallest prime number that begins a prime gap of at least 2n)». The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

semanticscholar.org

api.semanticscholar.org

Bruins, Evert Marie, review in Mathematical Reviews of Gillings, R.J. (1974). «The recto of the Rhind Mathematical Papyrus. How did the ancient Egyptian scribe prepare it?». Archive for History of Exact Sciences. 12 (4): 291–298. doi:10.1007/BF01307175. MR 0497458. S2CID 121046003.
Katz, Shaul (2004). «Berlin roots – Zionist incarnation: the ethos of pure mathematics and the beginnings of the Einstein Institute of Mathematics at the Hebrew University of Jerusalem». Science in Context. 17 (1–2): 199–234. doi:10.1017/S0269889704000092. MR 2089305. S2CID 145575536.
Mackinnon, Nick (1987 թ․ հունիս). «Prime number formulae». The Mathematical Gazette. 71 (456): 113–114. doi:10.2307/3616496. JSTOR 3616496. S2CID 171537609.
Green, Ben; Tao, Terence (2008). «The primes contain arbitrarily long arithmetic progressions». Annals of Mathematics. 167 (2): 481–547. arXiv:math.NT/0404188. doi:10.4007/annals.2008.167.481. S2CID 1883951.

uwaterloo.ca

cs.uwaterloo.ca

Caldwell, Chris K.; Reddick, Angela; Xiong, Yeng; Keller, Wilfrid (2012). «The history of the primality of one: a selection of sources». Journal of Integer Sequences. 15 (9): Article 12.9.8. MR 3005523. For a selection of quotes from and about the ancient Greek positions on the status of 1 and 2, see in particular pp. 3–4. For the Islamic mathematicians, see p. 6.
Caldwell, Chris K.; Xiong, Yeng (2012). «What is the smallest prime?» (PDF). Journal of Integer Sequences. 15 (9): Article 12.9.7. MR 3005530.

web.archive.org

Ramaré, Olivier (1995). «On Šnirel'man's constant». Annali della Scuola Normale Superiore di Pisa. 22 (4): 645–706. MR 1375315. Արխիվացված է օրիգինալից 2022 թ․ փետրվարի 9-ին. Վերցված է 2018 թ․ հունվարի 23-ին.

worldcat.org

Adler, Irving (1960). The Giant Golden Book of Mathematics: Exploring the World of Numbers and Space. Golden Press. էջ 16. OCLC 6975809.
Beiler, Albert H. (1999) [1966]. Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover. էջ 2. ISBN 978-0-486-21096-4. OCLC 444171535.
Euclid's Elements, Book IX, Proposition 20. See David Joyce's English translation of Euclid's proof or Williamson, James (1782). The Elements of Euclid, With Dissertations. Oxford: Օքսֆորդի համալսարանի հրատարակչություն. էջ 63. OCLC 642232959.