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CHAP, xiii]             FACTOR TABLES, LISTS OF PBIMES.                        351
P. Barlow46 gave the prime and power of prime factors of numbers to 10000 and a list of primes to 100 103.
G. Hutton47 gave the least factor of numbers to 10000.
Rees' Cyclopaedia, 1819, vol. 28, lists the primes to 217 219.
Peter Barlow48 gave a two-page table for finding factors of a number N< 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 hi 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. Kulik49 gave a factor table to 1 million.
J. Hantschl60 gave a factor table to 18277; J. M. Salomon,51 to 102011.
A. L. Crelle52 gave the number of primes 4n+1 and the number of prunes 4n+3 in each thousand up to the fiftieth.
A. Guyot53 listed the primes to 100 000.
A. F. Mobius,53a 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 lie in straight lines, others in parabolas, etc.
P. A. G. Colombier536 discussed the determination of the prunes <f, given those < L
H. G. Kohler64 gave a factor table to 21524.
E.  Hinkley56 gave a factor table to 100 000, listing all factors of odd numbers to 20000 and of even numbers to 12500.
F. Schallen55agave the prime and prime-power factors of numbers < 10000. F. Landry56 gave factor and prime tables to 10000.
A. L. Crelle57 discussed the expeditious construction of a factor table, and in particular a method of extending Chernac's44 table to 7 million. J. Hoiiel58 gave a factor table to 10841. Jacob Philip Kulik (1773-1863) spent 20 years constructing a factor
46New Mathematical Tables, London, 1814.    Errata, Cunningham.86
"Phil and Math. Dictionary, 1815, vol. 2, 236-8.
48New Series of Math. Repository (ed., Th. Leybourn), London, 4, 1819, II, 30-39.
49Tafeln der einfachen Faktoren aller Zahlen unter 1 million, Graz, 1825.
»°Log.-trig. Handbuch, Wien, 1827.                                          "Log. Tafeln, Wien, 1827.
MJour. fur Math., 10, 1833, 208.
"The'orie ge"nexale de la divisibility des nombres, suivie d'applications varie"es et d'une table de
nombres premiers compris entre 0 et 100 000, Paris, 1835.
"ojour. fur Math., 22, 1841, 276-284.                         M6Nouv. Ann. Math., 2, 1843, 408-410.
MLog.-trig. Handbuch, Leipzig, 1848.   Errata, Cunningham.85 "Tables of the prime numbers and prime factors of the composite numbers from 1 to 100 000,
Baltimore, 1853.    Reproduction of Brancker's8 table.
B6aPrimzahlen-Tafel von 1 bis 10000..., Weimar, 1855.    For 99 errata, see Cunningham.85 "Tables des nombres entiers non divisibles par 2, 3, 5, et 7, jusqu' a 10201, avec leurs diviseurs
simples en regard, et des Carre's des 1000 premiers nombres, Paris, 1855.    Tables des
nombres premiers, de 1 & 10000, Paris, 1855. 67Jour. fur Math., 51, 1856, 61-99.                                        "Tables de log., Paris; 1858.