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348                          HlSTOKY OF THE THEOKY OF  NUMBEKS.              [CHAP. XIII
D. Schwenter9 gave all the factors of the odd numbers < 1000.
John Wallis10 gave a list of errata in Brancker's8 table.
John Harris,11 D. D., F. R. S., reprinted Brancker's8 table.
De Traytorens12 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. Poetius13 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,14 Willigs,19 and Lambert.22
Johann Gottlob Krtiger15 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 Ntirnberg.
James Dodson16 gave the least divisors of numbers to 10000 not divisible y 2 or 5 and the primes from 10000 to 15000.
Etienne Francois du Tour17 described the construction of a table of all composite odd numbers to 10000 by multiplying 3,5,..., 3333 by 3,..., 99.
Giuseppe Pigri18 gave all prime factors of numbers to 10000.
Michel Lorenz Willigs19 (Willich) gave all divisors of numbers to 10000.
Henri Anjema20 gave all divisors of numbers to 10000.
Rallier des Ourmes21 gave as if new the sieve of Eratosthenes, placing 3 above 9 and every third İdd number after it, a 7 above 49, etc. He expressed each number up to 500 as a product of powers of primes.
J. H. Lambert22 described a method of making a factor table and gave Poetius'13 table and expressed a desire for a table to 102 000. Lagrange called his attention to Brancker's8 table.
Lambert23 gave [Kriiger's15] table showing the least factor of numbers not divisible by 2,3, 5 up to 102000, and a table of primes to 102 000, errata in which were noted by Kltigel24.
"Geometria Practiea, Numb., 1667,1, 312.
"Treatise 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.    Wallis, Opera, 2, 511, listed 30 errors. 12Histoire de 1'Acad. Roy. Science, anne*e 1717, Paris, 1741, Hist., 42-47. "Anleitung zu der Arith. Wissenschaft vermittelst einer parallel Algebra, Frkf. u. Leipzig, 1728. "Vollst. 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.23
"The Calculator.. .Tables for Computation, London, 1747. "Histoire de TAcad. Roy. So., Paris, annSe 1754, Hist., 88-90. 18Nuove tavole degli elementi dei numeri dair 1 al 10 000, Pisa, 1758. 19Grundliche Vorstellung der Reesischen allgemeinen Regel.. .Rechnungsarten,  Bremen u.
Gottingen, 2, 1760, 831-976.
20Table des diviseurs de tous les nombres naturels, depuis 1 jusqu'a 10 000, Ley den, 1767,302 pp. 21Me"m. de math, et de physique, Paris, 5, 1768, 485-499.
"Beytrage zum Gebrauche der Math. u. deren Anwendung, Berlin, 1770, II, 42. 23Zusatze zu den logarithmischen und trig. Tabellen, Berlin, 1770. MMath. Worterbuch, 3, 1808, 89^-900.