•'I;i Chap. XIII] FACTOR TABLES, LiSTS OF PrIMES. 351 
P. Barlow^® gave the prime and power of prime factors of numbers to 
10000 and a list of primes to 100 103. 
C. Hutton^^ gave the least factor of numbers to 10000. 
Rees' Cyclopaedia, 1819, vol. 28, Hsts the primes to 217 219. 
Peter Barlow^^ gave a two-page table for finding factors of a number 
iV< 100 000. The primes p = 7 to p = 313 are at the head of the columns, 
while the 18 numbers 1000, . . . , 9000, 10000, 20000, . . . , 90000 are in the left- 
hand column. In the body of the table is the remainder of each of the 
latter when divided by the primes p. To test if p is a factor of N, add its 
last two digits to the remainders in the line of hundreds and thousands in 
the column headed p and test whether the sum is divisible by p. 
J. P. Kulik'^^ gave a factor table to 1 million. 
J. HantschP° gave a factor table to 18277; J. M. Salomon,^^ to 102 Oil. 
A. L. Crelle^^ gave the number of primes 4n+ 1 and the number of primes 
4n+3 in each thousand up to the fiftieth. 
A. Guyot^^ hsted the primes to 100 000. 
A. F. Mobius,^^" using square ruled paper, inserted from right to left 
0, 1, 2, ... in the top row of cells, and inserted n in each cell of the nth row 
below the top row whenever the corresponding number in the top row is 
divisible by n. We thus have a factor table. Certain numbers of the table 
Ue in straight lines, others in parabolas, etc. 
P. A. G. Colombier^^^ discussed the determination of the primes <V, 
given those < I. 
H. G. Kohler'^ gave a factor table to 21524. 
E. Hinkley^^ gave a factor table to 100 000, listing all factors of odd 
numbers to 20000 and of even numbers to 12500. 
F. Schallen^^"gave the prime and prime-power factors of numbers < 10000. 
F. Landry^*^ gave factor and prime tables to 10000. 
A. L. Crelle^^ discussed the expeditious construction of a factor table, and 
in particular a method of extending Chernac's^ table to 7 million. 
J. HoiieP^ gave a factor table to 10841. 
Jacob Philip Kulik (1773-1863) spent 20 years constructing a factor 
*^New Mathematical Tables, London, 1814. Errata, Cunningham.^ 
<Thil. and Math. Dictionary, 1815, vol. 2, 236-8. 
^8New Series of Math. Repository (ed., Th. Leybourn), London, 4, 1819, II, 30-39. 
^'Tafeln der einfachen Faktoren aUer Zahlen unter 1 million, Graz, 1825. 
60Log.-trig. Handbuch, Wien, 1827. "Log. Tafeln, Wien, 1827. 
^2Jour. fur Math., 10, 1833, 208. 
'^Thdorie g^nerale de la divisibihte des nombres, suivie d'applications varices et d'une table de 
nombres premiers compris entre et 100 000, Paris, 1835. 
63a Jour, fvir Math., 22, 1841, 276-284. "^Nouv. Ann. Math., 2, 1843, 408-410. 
"Log.-trig. Handbuch, Leipzig, 1848. Errata, Cunningham.** 
^^Tables of the prime numbers and prime factors of the composite numbers from 1 to 100 000, 
Baltimore, 1853. Reproduction of Brancker's* table. 
ssaprirjizahlen-Tafel von 1 bis 10000. . ., Weimar, 1855. For 99 errata, see Cunningham.*^ 
6*Tables des nombres entiers non divisibles par 2, 3, 5, et 7, jusqu' k 10201, avec leurs diviseurs 
simples en regard, et des carres des 1000 premiers nombres, Paris, 1855. Tables des 
nombres premiers, de 1 £l 10000, Paris, 1855. 
"Jour, ftir Math., 51, 1856, 61-99. "Tables de log., Paris, 1858. 
