Chap. XIII] FACTOR TABLES, LiSTS OF PrIMES. 349 
J. Ozanam^^ gave a table of primes to 10000. 
A. F. Marci^^ gave in 1772 a list of primes to 400 000. 
Jean Bernoulli^^" tabulated the primes 16n+l up to 21601. 
L. Euler" discussed the construction of a factor table to one miUion. 
Given a prime p = 30a±i (^ = 1, 7, 11, 13), he determined for each r = l, 7, 
11, 13, 17, 19, 23, 29, the least q for which SOq+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. Hindenburg^^ 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. FelkeP^ 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 manuscript^", 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.^^] 
L. Bertrand^^ discussed the construction of factor tables. 
The Encyclopedie of d'Alembert, ed. 1780, end of vol. 2, contains a 
factor table to 100 000. 
Franz Schaffgotsch^^ 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 
SOm+k, /c = 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 Lambert^^ that some one should construct a fac- 
tor table to one million led L. Oberreit, von Stamford, Rosenthal, Felkel, 
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 
^^Recreations Math., new ed., Paris, 1723, 1724, 1735, etc., I, p. 47. 
^^Primes "in quater centenis millibus," Amstelodami, 1772. 
26aNouv. M6m. Ac. Berlin, ann^e 1771, 1773, 323. 
"Novi Comm. Acad. Petrop., 19, 1774, 132; Comm. Arith., 2, 64. 
''^Beschreibung einer ganz neuen Art nach einem bekannten Gesetze fortgehende Zahlen durch 
Abzahlen oder Abmessen bequem u. sicher zu finden. Nebst Anwendung der Methode 
auf verschiedene Zahlen, besonders auf eine damach zu fertigende Factorentafel . . . , 
Leipzig, 1776, 120 pp. 
2*Tabula omnium factorum simphcium, numerorum 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 hbraries of the Royal Society 
of London and Gottingen University. 
"Cf. Zach's Monatliche Correspondenz, 2, 1800, 223; Allgemeine deutsche BibUothek, 33, II, 495. 
'^Develop, nouveau de la partie ^1. math., Geneve, 1774. 
'''Gesetz, welches zur Fortsetzung der bekannten Pellischen Tafehi dient, Abhand. Privatgesell- 
schaft in Bohmen, Prag, 5, 1782, 354-382. 
