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Full text of "History Of The Theory Of Numbers - I"

350                   HISTORY OP THE THEORY OF NUMBERS.          [CHAP, xin
million. Their extended correspondence with Lambert33 was published. Of the tables constructed by these computers, the only one published is that by Felkel.29 The history of their connection with factor tables has been treated by J. W. L. Glaisher,34
Johann Neumann35 gave all the prime factors of numbers to 100 100.
Desfaviaae gave a like table in the same year.
F. Maseres36 reprinted the table of Brancker.8
G. Vega37 gave all the prime factors of numbers not divisible by 2, 3, or 5 to 102 000 and a list of primes from 102 000 to 400 031. Chernac listed errors in both tables.   In Hiilsse's edition, 1840, of Vega, the list of primes extends to 400 313.
A. Felkel,38 in his Latin translation of Lambert's23 Zusatze, gave all the prune factors except the greatest of numbers not divisible by 2, 3, 5 up to 102 000, large primes being denoted by letters. In the preface he stated that, being unable to obtain his extensive manuscript30 in 1785, he calculated again a factor table from 408 000 to 2 856 000.
J. P. Griison39 gave all prime factors of numbers not divisible by 2, 3, 5 to 10500. He39a gave a table of primes to 10000.
F. W. D. Snell40 gave the prime factors of numbers to 30000.
A. G. Kastner41 gave a report on factor tables.
K C. F. Krause42 gave a table of 22 pages showing all products < 100 000 of two primes, a table of primes < 100 000 with letters for 01, 03,..., 99, and (pp. 25-28) a factor table to 10000 by use of letters for numbers < 100.
N. J. Lidonne43 gave all prime factors of numbers to 102 000.
Jacob Struve43a made a factor table to 100 by de Traytorens'12 method.
L. Chernac44 gave all the prime factors of numbers, not divisible by 2, 3 or 5, up to 1 020 000.
J. C. Burckhardt46 gave the least factor of numbers to 3 million. He did not compute the first million, but compared ChernacJs table with a manuscript (mentioned in Briefwechsel,33 p. 140) by Schenmarck which extended to 1 008 000. Cf. Meissel.66
33 Job. Heinrich Lamberts deutscher gelehrter Brief wechsel, herausgegeben von Joh. Bernoulli,
Berlin, 1785, Leipzig, 1787, vol. 5.            "Proc. Cambridge Phil. Soc., 3, 1878, 99-138.
"Tabellen der Primzahlen und der Faktoren der Zahlen, welche unter 100 100, und durch 2, 3
oder 5 nicht theilbar sind, Dessau, 1785, 200 pp. "The Doctrine of Permutations and Combinations..., London, 1795. 'Tabulae logarithmico-trigonometricae, 1797, vol. 2. 88J. H. Lambert, Supplementa tab. log. trig., Lisbon, 1798. "Pmacotheque, ou collection de Tables. .., Berlin, 1798. s9flEnthullte Zaubereyen u. Geheimnisse d. Arith., Berlin, 1796, I, 82-4. 40Ueber eine neue und bequeme Art, die Factorentafein einzurichten, nebst einer Kupfertafel
der einfachen Factoren von 1 bis 30000, Giessen and Darmstadt, 1800. "Fortsetzung der Rechenkunst, ed. 2, Gottingen, 1801, 566-582.
42Factoren- und Primzahlentafel von 1 bis 100 000 neu berechnet, Jena u. Leipzig, 1804. "Tables de tous les diviseurs des nombres <102 000, Paris, 1808. *30Handbuch der Math., Altona, II, 1809, 108. 44Cribrum Arithmeticum... Daventrise, 1811, 1020 pp.    Reviewed by Gauss, Gottingische
gelehrte Anzeigen, 1812; Werke 2, 181-2.   Errata, Cunningham.86 "Tables des diviseurs... 1 a 3 036 000, Paris, 1817,1814, 1816 (for the respective three millions),
and 1817 (in one volume).