Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

How was $F_ 6$ factored?
HTML articles powered by AMS MathViewer

by H. C. Williams PDF
Math. Comp. 61 (1993), 463-474 Request permission

Abstract:

In 1880 at the age of 82 FortunĂ© 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
    Anonymous, DĂ©composition de ${2^{64}} + 1$, Nouv. Corresp. Math. 6 (1880), 417. 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. P. Fermat, Fragment d’une lettre de Fermat, Oeuvres de Fermat 2 (1894), 256-258.
  • 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, DOI 10.1007/978-1-4939-7560-0
    • F. Landry, ProcĂ©dĂ©s nouveaux pour dĂ©montrer que le nombre 2147483647 est premier, Librarie Hachette, Paris, 1859; partially reprinted Sphinx-Oedipe 4 (1909), 6-9. —, Aux mathematiciens de toutes les parties du monde. Communication sur la dĂ©composition des nombres en leurs facteurs simples, Librairie Hachette, Paris, 1867. —, DĂ©compositions des nombres ${2^n} \pm 1$ en leurs facteurs premiers de $n = 1$ Ă  $n = 64$ (moins quatre), Librairie Hachette, Paris, 1869. —, Sur la dĂ©composition du nombre ${2^{64}} + 1$, C. R. Acad. Sci. Paris 91 (1880), 138. —, Letter addressed to Lucas dated July 7, 1880, Sphinx-Oedipe 18 (1923), 70-71. —, Letter to Charles Henry, Boll. di Biblio. Storia Sci. Mat. Fis. 13 (1880), 469-470. —, MĂ©thode de dĂ©composition des nombres en facteurs premiers, Assoc. Français Avance. Sci. Comptes Rendus 9 (1880), 185-189. —, Note d’algĂšbre, J. Math. ÉlĂ©mentaires et SpĂ©ciales 5 (1881), 3-9. E. Lucas, ConsidĂ©rations nouvelles sur la thĂ©orie des nombres premiers et sur la division gĂ©omĂ©trique de la circonfĂ©rence en parties Ă©gales, Assoc. Français Avanc. Sci. Comptes Rendus 6 (1877), 159-167. —, ThĂ©orĂšme d’arithmĂ©tique, Atti Reale Accad. Sci. Torino 13 (1877-8), 271-284.
  • Edouard Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math. 1 (1878), no. 4, 289–321 (French). MR 1505176, DOI 10.2307/2369373
    • —, Remarque, Nouv. Corresp. Math. 4 (1878), 285. —, RĂ©crĂ©ations mathĂ©matiques, vol. 2, 2nd ed., Paris, 1891, pp. 230-235. T. Pepin, Sur la dĂ©composition 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
  • © Copyright 1993 American Mathematical Society
  • Journal: Math. Comp. 61 (1993), 463-474
  • MSC: Primary 01A55; Secondary 11-03
  • DOI: https://doi.org/10.1090/S0025-5718-1993-1182248-9
  • MathSciNet review: 1182248