1878.] Mr Glaisher, On factor tables. 103 



may be obtained by simple addition. Similarly, Wolfram's table 

 gives 48-decimal hyperbolic logarithms of primes up to 10,009. 

 Thus a factor table forms a very valuable complement to many- 

 place logarithmic tables, the range of which must necessarily be 

 comparatively limited ; and even in the case of large prime 

 numbers, or numbers exceeding the limits of the factor table, it 

 affords a very convenient method of calculating logarithms. An 

 example to illustrate this application of the table is given in an 

 appendix to this paper (§ 21). 



But, independently of these applications of the table, the reso- 

 lution of a number into its factors is so elementary and funda- 

 mental an operation, but withal so difficult in individual cases, 

 that a factor table may well be regarded as both a collection of 

 valuable facts, and as a table interesting in itself. It is not sur- 

 prising, therefore, that the formation and extension of such tables 

 have long engaged the attention of mathematicians, and that a 

 great amount of labour has been devoted to this object. 



§ 3. The following works, &c., are described by Chernac in 

 Part III. of the Introduction to his Crihrum Arithmeticum (1811). 



1657. Francis Schooten. List of primes to 10,000. 



1668. Pell (in Branch er's translation of Ehonius's Algebra, 

 published at London). Least divisors of numbers no,t divisible by 

 2 or 5, to 100,000. 



1717. De Traytorens. Exhibits to the French Academy a 

 method of making factor tables. 



1728. Poetius (in his Arithmetic, Leipzig). An "■ anatome ' of 

 numbers to 10,000. Reprinted by Richter in t. ii. of his mathe- 

 matical Lexicon. 



1746. Krliger. Table of primes to 101,000'. Calculated by 

 Peter Jager. 



1767. Anjema. Factor table to 10,000. All divisors (prime 

 and composite) given. Table occupies 802 quarto pages. This 

 was a posthumous work. Anjema had intended the table to 

 extend to 100,000. 



1768. Rallier Des Ourmes. Communicates to the French 

 Academy a method of finding factors of numbers. 



1770. Lambert (in his Zusdtze zu den...Tabellen, Berlin). 

 Least factors of numbers not divisible by 2, 3, or 5 to 102,000 ; 

 and list of primes to 102,000. 



1772. Marci. List of primes to 400,000. 



1774. Euler. Memoir on the construction of a factor table to 

 extend to a million. 



1778. Bertrand. Remarks on the formation of factor tables. 



1 The title-page lias " Primzalilen von 1 bis 1000000" but the list ends with 

 100,999. (Brit. Assoc. Report, p. 35.) 



