350 History of the Theory of Numbers. [Chap, xiii | '^ ' 
million. Their extended correspondence with Lambert^^ was published. 
Of the tables constructed by these computers, the only one published is that 
by Felkel.-^ The history of their connection with factor tables has been 
treated by J. W. L. Glaisher.^ 
Johann Neumann^^ gave all the prime factors of numbers to 100 100. 
Desfaviaae gave a like table in the same year. 
F. Maseres^^ reprinted the table of Brancker.^ 
G. Vega^^ 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 hsted errors 
in both tables. In Hiilsse's edition, 1840, of Vega, the Ust of primes extends 
to 400 313. 
A. Felkel,^^ in his Latin translation of Lambert's'^^ Zusatze, gave all the 
prime 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 manuscript^" in 1785, he calculated 
again a factor table from 408 000 to 2 856 000. 
J. P. Griison^^ gave all prime factors of numbers not divisible by 2, 3, 5 
to 10500. He^^'' gave a table of primes to 10000. 
F. W. D. Snell^° gave the prime factors of numbers to 30000. 
A. G. Kastner^^ gave a report on factor tables. 
K. C. F. Krause'*- 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. Lidonne^^ gave all prime factors of numbers to 102 000. 
Jacob Struve"*^" made a factor table to 100 by de Traytorens'^^ method. 
L. Chernac^ gave all the prime factors of numbers, not divisible by 
2, 3 or 5, up to 1 020 000. 
J. C. Burckhardt*^ gave the least factor of numbers to 3 million. He did 
not compute the first million, but compared Chernac's table with a manu- 
script (mentioned in Briefwechsel,^^ p. 140) by Schenmarck which extended 
to 1 008 000. Cf. iVIeissel.''^ 
^'Joh. Heinrich Lamberts deutscher gelehrter Briefwechsel, herausgegeben von Joh. Bernoulli, 
Berlin, 1785, Leipzig, 1787, vol. 5. "Proc. Cambridge Phil. Soc, 3, 1878, 99-138. 
'^Tabellen der Primzahlcn 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. 
**J. H. Lambert, Supplementa tab. log. trig., Lisbon, 1798. 
"Pinaeoth6que, ou collection de Tables. . ., Berlin, 1798. 
''"Enthiillte Zaubereyen u. Geheimnisse d. Arith., Berlin, 1796, I, 82-4. 
*°Ueber eine neue und bequeme Art, die Factorentafeln einzurichten, nebst einer Kupfertafel 
der einfachen Factoren von 1 bis 30000, Gicssen and Darmstadt, 1800. 
"Fortsetzung der Rechenkunst, ed. 2, Gottingen, 1801, 566-582. 
^'Factoren- und Primzahlentafel von 1 bis 100 000 neu berechnet, Jena u. Leipzig, 1804. 
"Tables de tous les diviseurs des nombres < 102 000, Paris, 1808. 
^'''Handbuch der Math., Altona, II, 1809, 108. 
**Cribrum Arithmeticum . . . Daventriae, Isil, 1020 pp. Reviewed by Gauss, Gottingische 
gelehrte Anzeigen, 1812; Werke 2, 181-2. Errata, Cunningham.*' 
"Tables des diviseurs. . . 1 ^ 3 036 000, Paris, 1817, 1814, 1816 (for the respective three milliona), 
and 1817 (in one volume). 
