History Of The Theory Of Numbers - I

CHAP, xiii] FACTOR TABLES, LISTS OF PRIMES. 349
J. Ozanam26 gave a table of primes to 10000.
A. F. Marci26 gave in 1772 a list of primes to 400 000.
Jean Bernoulli260 tabulated the primes 16n+l up to 21601.
L. Euler27 discussed the construction of a factor table to one million. Given a prime p = 3Qa=±t (t=l, 7, 11, 13), he determined for each r=l, 7, 11, 13, 17, 19, 23, 29, the least q for which 30g-f r is divisible by p, and arranged the results in a single table with p ranging over the primes from 7 to 1000. He showed how to use this auxiliary table to construct a factor table between given limits.
C. F. Hindenburg28 employed in the construction of factor tables a "patrone" or strip of thick paper with holes at proper intervals to show the multiples of p, for the successive primes p.
A. Felkel29 gave in 1776 a table of all the prime factors (designated by letters or pairs of letters) of numbers, not divisible by 2, 3, or 5, up to 408 000, requiring for entry two auxiliary tables. In manuscript30, the table extended to 2 million; but as there were no purchasers of the part printed, the entire edition, except for a few copies, was used for cartridges in the Turkish war. The imperial treasury at Vienna, at the cost of which the table was printed, retained the further manuscript. [See Felkel.38]
L. Bertrand31 discussed the construction of factor tables.
The Encyclopedic of d'Alembert, ed. 1780, end of vol. 2, contains a factor table to 100 000.
Franz Schaffgotsch32 gave a method, equivalent to that of a stencil for each prime p, for entering the factor p in a factor table with eight headings 30m+fc, A; = 1, 7, 11, 13, 17,19, 23, 29, and hence of numbers not divisible by 2, 3, or 5. Proofs were given by Beguelin and Tessanek, ibid., 362, 379.
The strong appeals by Lambert23 that some one should construct a factor table to one million led L. Oberreit, von Stamford, Rosenthal, Felkei, and Hindenburg to consider methods of constructing factor tables and to prepare such tables to one million, with plans for extension to 5 or 10
26Recreations Math., new ed., Paris, 1723, 1724, 1735, etc., I, p. 47.
26Primes "in quater centenis millibus," Amstelodami, 1772.
2«aNouv. M6rn. Ac. Berlin, anne"e 1771, 1773, 323.
27Novi Comm. Acad. Petrop., 19, 1774, 132; Comm. Arith., 2, 64.
28Beschreibung einer ganz neuen Art nach einem bekannten Gesetze fortgehende Zahlen durch
Abziihlen odcr Abmessen bequem u. sicker zu finden. Nebst Anwendung der Methode
auf verschiedene Zahlen, besonders auf eine daraach zu fertigende Factorentafel...,
Leipzig, 1776, 120 pp. 20Tabula omnium factorum eimplicium, numerorurn per 2, 3, 5 non divisibilium ab 1 usque
10 000 000 [!]. Elaborata ab Antonio Felkel. Pars I. Exhibens factores ab 1 usque
144 000, Vindobonae, 1776. Then there is a table to 408 000, given in three sections.
There is a copy of this complete table in the Graves Library, University College, London.
Tafel aller einfachen Factoren der durch 2, 3, 5 nicht theilbaren Zahlen von 1 bis 10 000 000.
Entworfen von Anton Felkel. I. Theil. Enthaltend die Factoren von 1 bis 144 000,
Wien, 1776. There is a copy of this incomplete table in the libraries of the Royal Society
of London and Gottingen University.
30Cf. Zach's Monatliche Corresponded, 2,1800,223; Allgemeine deutsche Bibliothek, 33, II, 495. 31Develop. nouveau de la partie el. math., Geneve, 1774. 32Gesetz, welches zur Fortsetzung der bekannten Pellischen Tafeln dient, Abhand. Privatgesell-
schaft in Bohmen, Prag, 5, 1782, 354-382.