Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

How was $ F\sb 6$ factored?


Author: H. C. Williams
Journal: Math. Comp. 61 (1993), 463-474
MSC: Primary 01A55; Secondary 11-03
MathSciNet review: 1182248
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In 1880 at the age of 82 Fortuné Landry factored the 20 digit number $ {F_6} = {2^{64}} + 1$. How did he do it? Landry himself never described how he factored $ {F_6}$; however, he did leave enough clues in his work and letters to provide some indication of the ideas with which he was working. In this paper we present a likely reconstruction of Landry's technique.


References [Enhancements On Off] (What's this?)

  • [1] Anonymous, Décomposition de $ {2^{64}} + 1$, Nouv. Corresp. Math. 6 (1880), 417.
  • [2] L. E. Dickson, History of the theory of numbers, Vol. 1: Divisibility and primality, Carnegie Inst. of Washington, Publ. No. 256 (1919); reprinted by Chelsea Books, New York, 1971.
  • [3] P. Fermat, Fragment d'une lettre de Fermat, Oeuvres de Fermat 2 (1894), 256-258.
  • [4] Carl Friedrich Gauss, Disquisitiones arithmeticae, Springer-Verlag, New York, 1986. Translated and with a preface by Arthur A. Clarke; Revised by William C. Waterhouse, Cornelius Greither and A. W. Grootendorst and with a preface by Waterhouse. MR 837656 (87f:01105)
  • [5] F. Landry, Procédés nouveaux pour démontrer que le nombre 2147483647 est premier, Librarie Hachette, Paris, 1859; partially reprinted Sphinx-Oedipe 4 (1909), 6-9.
  • [6] -, Aux mathematiciens de toutes les parties du monde. Communication sur la décomposition des nombres en leurs facteurs simples, Librairie Hachette, Paris, 1867.
  • [7] -, Décompositions des nombres $ {2^n} \pm 1$ en leurs facteurs premiers de $ n = 1$ à $ n = 64$ (moins quatre), Librairie Hachette, Paris, 1869.
  • [8] -, Sur la décomposition du nombre $ {2^{64}} + 1$, C. R. Acad. Sci. Paris 91 (1880), 138.
  • [9] -, Letter addressed to Lucas dated July 7, 1880, Sphinx-Oedipe 18 (1923), 70-71.
  • [10] -, Letter to Charles Henry, Boll. di Biblio. Storia Sci. Mat. Fis. 13 (1880), 469-470.
  • [11] -, Méthode de décomposition des nombres en facteurs premiers, Assoc. Français Avance. Sci. Comptes Rendus 9 (1880), 185-189.
  • [12] -, Note d'algèbre, J. Math. Élémentaires et Spéciales 5 (1881), 3-9.
  • [13] E. Lucas, Considérations nouvelles sur la théorie des nombres premiers et sur la division géométrique de la circonférence en parties égales, Assoc. Français Avanc. Sci. Comptes Rendus 6 (1877), 159-167.
  • [14] -, Théorème d'arithmétique, Atti Reale Accad. Sci. Torino 13 (1877-8), 271-284.
  • [15] Edouard Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math. 1 (1878), no. 4, 289–321 (French). MR 1505176, http://dx.doi.org/10.2307/2369373
  • [16] -, Remarque, Nouv. Corresp. Math. 4 (1878), 285.
  • [17] -, Récréations mathématiques, vol. 2, 2nd ed., Paris, 1891, pp. 230-235.
  • [18] T. Pepin, Sur la décomposition des grands nombres en facteurs premiers, Atti Accad. Pontificia dei Nuovi Lincei 43 (1889-90), 163-191.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 01A55, 11-03

Retrieve articles in all journals with MSC: 01A55, 11-03


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1182248-9
PII: S 0025-5718(1993)1182248-9
Article copyright: © Copyright 1993 American Mathematical Society