[1] L. E. Dickson, “History of the Theory of Numbers, I: Divisibility and Primality,” G. E. Stechert & Co., New York, 1934.
[2] J. Derbyshire, “Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics,” Joseph Henry Press, Washington DC, 2003.
[3] M. du Sautoy, “The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics,” Harper Collins Publishers, New York, 2003.
[4] D. Wells, “Prime Numbers: The Most Mysterious Figures in Math,” John Wiley & Sons, Inc., Hoboken, NJ, 2005.
[5] L. Depuydt, “The Mathematical and Physical Theory of Rational Human Intelligence: Complete Empirical-Digital Properties; Full Electrochemical-Mechanical Model (Part I: Mathematical Foundations),” Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 3, No. 5 (August 2013), pp. 491-561; bibliographical references to earlier publications pertaining to the larger project are listed there. The following typos appear in this article (references are to page, column, and line): (506,a,11) for “or modern” read “of modern”; (513,a,30) for “chose” read “choose”; (515,a,10 counting from bottom) for “and” read “an”; (546,b,19) for “incrase” read “increase”; (552,b,30) for “describe” read “described”; (554,a,34) for “Maxwell’s” read “Maxwell” (555,b,37) for “interested” read “interest”; (559,a,note 14,1]) for “P. E. B. Jourdain” read “Ph. E. B. Jourdain”; (559,b,note 67,3). Also, at 553,a,3, for “below” read “in later articles.”
[6] As for CerDi, see L. Depuydt, “The Other Mathematics,” Gorgias Press, Piscataway, NJ, 2008, especially at pp. 79-95 and pp. 307-321.
[7] As for SupDi, see L. Depuydt, “Zur unausweichlichen Digitalisierung der Sprachbetrachtung: ‘Allein’, ‘anderer’, ‘auch’, ‘einziger’, ‘(seiner)seits’, und ‘selbst’ als digitales Wortfeld im Agyptisch-Koptischen und im Allgemeinen [On the Unavoidable Digitalization of Language Analysis: ‘Alone’, ‘Other’, ‘Also’, ‘Only’, ‘On (His) Part’, and ‘Self’ as Digital Semantic Field in Egyptian-Coptic and in General],” In: A. I. Blobaum, K. Butt, and I. Kohler, Eds., Lexical Fields, Semantics and Lexicography, Aegyptiaca Monasteriensia, Vol. 7, Shaker Verlag, Aachen, 2011, pp. 5-38.
[8] www.oeis.org. Search for “A231273” and “A231327.”
[9] M. du Sautoy, “The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics,” Harper Collins Publishers, New York, 2003, p. 314.
[10] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 2, Dover Publications, New York, 1956, p. 278.
[11] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, p. 153.
[12] J. Derbyshire, “Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics,” Joseph Henry Press, Washington DC, 2003, p. 9.
[13] J. Derbyshire, “Prime Obsession,” Joseph Henry Press, Washington DC, 2003, pp. 63-65.
[14] J. Derbyshire, “Prime Obsession,” Joseph Henry Press, Washington DC, 2003, pp. 102-107.
[15] B. Riemann, “über die Anzahl der Primzahlen unter einer gegebenen Grosse,” Monatsberichte der Koniglichen Preussischen Akademie der Wissenschaften zu Berlin: Aus dem Jahre 1859, F. Dümmler, Berlin, 1860, pp. 671-680.?
[16] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960, p. 4.
[17] http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/03/02 (accessed last on October 31, 2013).
[18] L. Euler, “Elements of Algebra,” Springer Verlag, New York, Berlin, Heidelberg, and Tokyo, 1984 (reprint of the English translation of 1840 by J. Hewlett of, [1], the French translation by J. Bernoulli (III) of the original German edition of 1770 and of, [2], the French additions by J.-L. Lagrange, with a preface by C. Truesdell that earlier appeared in H. E. Pagliaro, Ed., “Irrationalism in the Eighteenth Century,” The Press of Case Western Reserve University, Cleveland and London, 1972, pp. 51-95), p. 92.
[19] D. Wells, “Prime Numbers: The Most Mysterious Figures in Math,” John Wiley & Sons, Inc., Hoboken, NJ, 2005, p. 69.
[20] B. Riemann, “über die Anzahl der Primzahlen unter einer gegebenen Grosse,” Monatsberichte der Koniglichen Preussischen Akademie der Wissenschaften zu Berlin: Aus dem Jahre 1859, F. Dümmler, Berlin, 1860, pp. 671-680, at p. 671.
[21] J. Derbyshire, “Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics,” Joseph Henry Press, Washington DC, 2003, p. 327.
[22] P. J. Nahin, “An Imaginary Tale: The Story of ,” Princeton University Press, Princeton and London, p. 173.
[23] http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/03/02 (accessed last on October 31, 2013).
[24] For the Greek text, see Aristotle, “Metaphysics Books I-IX,” with an English translation by H. Tredennick, Loeb Classical Library, Vol. 271, Harvard University, Cambridge, MA, 1933, p. 160 and p. 162.
[25] M. Dehn, “Beziehungen zwischen der Philosophie und der Grundlegung der Mathematik im Altertum,” Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Vol. B.4.1, Julius Springer, Berlin, 1937, pp. 1-28, at p. 8.
[26] J.[-]L. Lagrange, Analytical Mechanics, Translated from the Mécanique analytique, no[u]velle edition of 1811, Translated and edited by A. Boissonnade and V. N. Vagliente, Boston Studies in the Philosophy of Science, Vol. 191, Kluwer Academic Publishers, Dordrecht/Boston/London, p. xii.
[27] J.[-]L. Lagrange, Analytical Mechanics, Translated and edited by A. Boissonnade and V. N. Vagliente, Boston Studies in the Philosophy of Science, Vol. 191, Kluwer Academic Publishers,
Dordrecht/Boston/London, 1997, p. 28.
[28] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960, pp. 273-296.
[30] W. A. Whitworth, Choice and Chance, with One Thousand Exercises, Hafner Publishing, New York and London, 1965, reprint of the fifth edition of 1901, pp. 93-96.
[31] J. E. Pommersheim, T. K. Marks, and E. L. Flapan, Number Theory: A Lively Introduction with Proofs, Applications, and Stories, John Wiley & Sons, Inc., Hoboken, NJ, 2010, p. 652.
[32] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960, p. 276.
[33] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960, p. 274.
[34] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960, p. 277.
[35] Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, p. 219.
[36] E. Beltrami, “Saggio di interpretazione della geometria non-euclidea,” Giornale di matematiche, Vol. 6, 1868, pp. 284-312 (a French translation appeared in Annales scientifiques de l’école Normale Supérieure, Series 1, Vol. 6, 1869, pp. 251-288).
[37] J. Hoüel, “Note sur l’impossibilité de démontrer par une construction plane le principe de la théorie des parallèles dit Postulatum d’Euclide,” Giornale di matematiche, Vol. 8, 1870, pp. 84-89.
[38] E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” Vol. 1, J. C. Hinrichs, Leipzig, 1890, p. 288.
[39] I. (Iohannes) L. Heiberg, Ed., “Euclidis Elementa,” Vol. II, B. G. Teubner, Leipzig, 1884, p. 186.
[40] E. S. Stamatis, Ed., after I. L. Heiberg, Ed., “Euclidis Elementa,” Vol. II, B. G. Teubner, Leipzig, 1970, p. 104.
[41] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 2, Dover Publications, New York, 1956, p. 277.
[42] Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 2, Dover Publications, New York, 1956, p. 279.
[43] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, p. 155.
[44] Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, pp. 202-220.
[45] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, p. 155.
[46] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, p. 154.
[47] Translation by Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 1, Dover Publications, New York, 1956, p. 312 and p. 342.
[48] J.-L. Lagrange, “Démonstration d’un théorème nouveau concernant les nombres premiers,” In: J.-A. Serret, Ed., Oeuvres de Lagrange, Vol. 3, Gauthier-Villars, Paris, 1869, pp. 425-438, at p. 425.
[49] J.-L. Lagrange, “Démonstration d’un théorème nouveau concernant les nombres premiers,” In: J.-A. Serret, Ed., Oeuvres de Lagrange, Vol. 3, Gauthier-Villars, Paris, 1869, pp. 425-438.
[50] L. E. Dickson, “History of the Theory of Numbers, I: Divisibility and Primality,” G. E. Stechert & Co., New York, 1934, p. 426.
[51] Th. L. Heath, “Euclid: The Thirteen Books of the Elements,” Vol. 2, Dover Publications, New York, 1956, p. 413.
[52] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960, p. 12.
[53] J. E. Pommersheim, T. K. Marks, and E. L. Flapan, Number Theory: A Lively Introduction with Proofs, Applications, and Stories, John Wiley & Sons, Inc., Hoboken, N. J., 2010, p. 105.
[54] L. E. Dickson, “History of the Theory of Numbers, I: Divisibility and Primality,” G. E. Stechert & Co., New York, 1934, p. 413.
[55] D. Wells, “Prime Numbers: The Most Mysterious Figures in Math,” John Wiley & Sons, Inc., Hoboken, NJ, 2005, p. 166.
[56] A. W. F. Edwards, “Pascal’s Arithmetical Triangle: The Story of a Mathematical Idea,” Johns Hopkins University Press, Baltimore, 2002.
[57] L. Euler, “Elements of Algebra,” Springer Verlag, New York, Berlin, Heidelberg, and Tokyo, 1984 (reprint of the English translation of 1840), p. 114.
[58] L. Depuydt, “The Mathematical and Physical Theory of Rational Human Intelligence,” Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 3, No. 5 (August 2013), pp. 491-561, at p. 577.
[59] Ch. Burney, “A General History of Music,” Vol. IV, Printed for the Author, London, 1789, p. 557.
[60] A. E. M. Grétry, “Mémoires ou essais sur la musique,” Vol. I, Printer of the Republic, Paris, Year 5 [of the French Republic], p. 424.
[61] G. Radiciotti, “G. B. Pergolesi: Vita, opere ed influenza su l’arte (con multi esempi musicali ed illustrazioni),” Edizione “Musica,” Rome, 1910.
[62] L. Depuydt, “The Mathematical and Physical Theory of Rational Human Intelligence,” Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 3, No. 5 (August 2013), pp. 491-561, passim.
[63] B. Mahon, “The Man Who Changed Everything,” John Wiley & Sons, Ltd, Chichester, West Sussex, 2004, especially at p. xi and pp. 176-185.
[64] B. Mahon, “The Man Who Changed Everything,” John Wiley & Sons, Ltd, Chichester, West Sussex, 2004, p. 176.
[65] C. B. Boyer, “A History of Mathematics,” Second Edition, John Wiley & Sons, Inc., New York, 1989, p. 490.
[66] J.[-]L. Lagrange, Analytical Mechanics, Translated and edited by A. Boissonnade and V. N. Vagliente, Boston Studies in the Philosophy of Science, Vol. 191, Kluwer Academic Publishers, Dordrecht/Boston/London, 1997, p. 28.
[67] Th. Hailperin, “Boole’s Logic and Probability” (First Edition), Studies in Logic and the Foundations of Mathematics, Vol. 85, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1976.
[68] Th. Hailperin, “Boole’s Logic and Probability,” Second edition, Revised and enlarged, Studies in Logic and the Foundations of Mathematics, Vol. 85, North-Holland Publishing Company, Amsterdam, New York, Oxford, and Tokyo, 1986.
[69] G. C. Smith, “The Boole-De Morgan Correspondence,” Clarendon Press, Oxford, 1982.
[70] D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985.
[71] I. Grattan-Guinness, “The Correspondence between George Boole and Stanley Jevons, 1863-1864,” History and Philosophy of Logic, Vol. 12, 1991, pp. 15-35. http://dx.doi.org/10.1080/01445349108837175
[72] I. Grattan-Guinness and G. Bornet, Eds., “George Boole: Selected Manuscripts on Logic and Its Philosophy,” Science Networks Historical Studies, Vol. 20, Birkhauser Verlag, Basel, Boston, and Berlin, 1997.?
[73] J. Gasser, Ed., “A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,” Kluwer Academic Publishers, Dordrecht, Boston, and London, 2000.
[74] M. H. Paymer and H. W. Williams, “Giovanni Battista Pergolesi: A Guide to Research,” Garland Composer Resources Manuals, Vol. 26, Garland Publishing Inc., New York and London, 1989.
[75] A. E. M. Grétry, “Mémoires ou essais sur la musique,” Vol. I, Printer of the Republic, Paris, Year 5 [of the French Republic], p. 424.
[76] Ch. Burney, “A General History of Music,” Vol. IV, Printed for the Author, London, 1789, p. 556.
[77] G. Radiciotti, “G. B. Pergolesi: Vita, opere ed influenza su l’arte (con multi esempi musicali ed illustrazioni),” Edizione “Musica,” Rome, 1910, p. 275.
[78] M. E. Paymer and H. W. Williams, “Giovanni Battista Pergolesi: A Guide to Research,” Garland Composer Resources Manuals, Vol. 26, Garland Publishing Inc., New York and London, 1989, p. 84.
[79] M. E. Paymer and H. W. Williams, “Giovanni Battista Pergolesi: A Guide to Research,” Garland Composer Resources Manuals, Vol. 26, Garland Publishing Inc., New York and London, 1989, p. 98.
[80] M. E. Paymer and H. W. Williams, “Giovanni Battista Pergolesi: A Guide to Research,” Garland Composer Resources Manuals, Vol. 26, Garland Publishing Inc., New York and London, 1989, p. 105.
[81] M. E. Paymer and H. W. Williams, “Giovanni Battista Pergolesi: A Guide to Research,” Garland Composer Resources Manuals, Vol. 26, Garland Publishing Inc., New York and London, 1989, p. 96.
[82] A. E. M. Grétry, “Mémoires ou essais sur la musique,” Vol. I, Printer of the Republic, Paris, Year 5 [of the French Republic], pp. 426-427.
[83] Ch. Burney, “A General History of Music,” Vol. IV, Printed for the Author, London, 1789, pp. 551-552.
[84] G. Radiciotti, “G. B. Pergolesi: Vita, opere ed influenza su l’arte (con multi esempi musicali ed illustrazioni),” Edizione “Musica,” Rome, 1910, p. 27.
[85] G. Radiciotti and A.-E. Cherbulliez, Ed., “Giovanni Battista Pergolesi: Leben und Werk,” Pan-Verlag, Zürich, 1954, p. 49.
[86] G. Radiciotti and A.-E. Cherbulliez, Ed., “Giovanni Battista Pergolesi: Leben und Werk,” Pan-Verlag, Zürich, 1954, see index at “Leo, L.”.