348 History of the Theory of Numbers. (Chap, xiii 
D. Schwenter^ gave all the factors of the odd numbers < 1000. 
John Wallis^° gave a list of errata in Brancker's^ table. 
John Harris," D. D., F. R. S., reprinted Brancker's^ table. 
De Traytorens^^ emphasized the utility of a factor table. To form a 
table showing all prime factors of numbers to 1000, begin by multiplying 
2, 3, .. . by all other primes < 1000, then multiply 2X3 by all the primes, 
then 2X3X5, etc. 
Joh. Mich. Poetius^^ gave a table (anatomiae numerorum) of all the 
prime factors of numbers, not divisible by 2, 3, 5, up to 10200. It was 
reprinted by Christian Wolf," Willigs,^^ and Lambert. ^- 
Johann Gottlob Krliger^* gave a table of primes to 100 999 (not to 1 
million, as in the title), stating that the table was computed by Peter 
Jager of Niirnberg. 
James Dodson^® gave the least di\'isors of numbers to 10000 not divisible 
by 2 or 5 and the primes from 10000 to 15000. 
Etienne FranQois du Tour^^ described the construction of a table of all 
composite odd numbers to 10000 by multiplying 3, 5, ... , 3333 by 3, ... , 99. 
Giuseppe Pigri^^ gave all prime factors of numbers to 10000. 
Michel Lorenz Willigs^^ (Willich) gave all di\dsors of numbers to 10000. 
Henri Anjema-° gave all divisors of numbers to 10000. 
Rallier des Ourmes-^ gave as if new the sieve of Eratosthenes, placing 
3 above 9 and every third odd number after it, a 7 above 49, etc. He 
expressed each number up to 500 as a product of powers of primes. 
J. H. Lambert^^ described a method of making a factor table and gave 
Poetius'^^ table and expressed a desire for a table to 102 000. Lagrange 
called his attention to Brancker's^ table. 
Lambert-^ gave [Ivriiger's^^] table showing the least factor of numbers 
not di\'isible by 2, 3, 5 up to 102000, and a table of primes to 102 000, errata 
in which were noted by KliigeP^. 
•Geometria Practica, Numb., 1667, I, 312. 
loTreatise of Algebra, additional treatise, Ch. Ill, §22, London, 1685. 
"Lexicon Technicum, or an Universal English Dictionary of Arts and Sciences, London, vol. 2, 
1710 (under Incomposite Numbers). In ed. 5, London, 2, 1736, the table was omitted, 
but the text describing it kept. WaUis, Opera, 2, ,511, listed 30 errors. 
"Histoire de I'Acad. Roy. Science, ann6e 1717, Paris, 1741, Hist., 42-47. 
"Anleitung zu der Arith. Wissenschaft vermittelst einer parallel Algebra, Frkf . u. Leipzig, 1728. 
"VoUst. Math. Lexicon, 2, Leipzig, 1742, 530. 
'*Gedancken von der Algebra, nebst den Primzahlen von 1 bis 1 000 000, Halle im Magd., 1746, 
Cf. Lambert. ^a 
"The Calculator. . .Tables for Computation, London, 1747. 
•"Histoire de I'Acad. Ro>. Sc, Paris, ann6e 1754, Hist., 8&-90. 
"Nuove tavole degli elementi dei numeri dall' 1 al 10 000, Pisa, 1758. 
"Griindhche Vorstellung der Reesischen allgemeinen Regel . . . Rechnungsarten, Bremen u. 
Gottingen, 2, 1760, 831-976. 
^Table des diviseurs de tous les nombres naturels, depuis 1 jusqu'4 10 000, Leyden, 1767, 302 pp. 
"M^m. de math, et de physique, Paris, 5, 1768, 485-499. 
"Bej-trage znm Gebrauche der Math. u. deren Anwendung, Berlin, 1770, II, 42. 
"Zusatze zu den logarithm ischen imd trig. Tabellen, BerUn, 1770. 
"Math. Worterbuch, 3, 1808, 892-900. 
