lOi Mr Glaisher, On factor tables. [Feb. 11, 



1785. Neumann. All prime factors of numbers, not divisible 

 by 2, 3, or 5, to 100,100. Table occupies 200 quarto pages. 



1797. Vega. All prime factors of numbers, not divisible by 

 2, 3, or 5, to 102,000; and a list of primes from 102,000 to 

 400,000. 



1804. Krause. Factor table to 100,000. Table occupies 28 

 folio pages. 



In preparing the British Association Report on Tables^ I met 

 with the following tables published previous to 1811, which are 

 not included in the above list. 



1659. Rahn. Least factors of numbers, not divisible by 2 or 

 5, to 24,000. Rahn is the same as Rhonius referred to under 

 Pell, 1668. 



1745. Dodson. Least factors of numbers, not divisible by 

 2 or 5, to 10,000. 



1758. Pigri. All prime factors of numbers to 10,000. 



1795. Maseres. Least factors of all numbers, not divisible by 

 2 or 5, to 100,000. Reprint of Brancker's table. See Pell, 1668. 



1798. Gruson. Prime factors of numbers, not divisible by 2, 3, 

 or 5, to 10,500. And I should also mention 



1800. Snell. Factor table to 30,000. This work I have not 

 seen, but only the title " Snell (F. W. D.), Ueber eine neue und 

 bequeme Art, die Factorentafeln einzurichten, nebst einer Kupfer- 

 tafel der einfachen Factoren von 1 bis 30000. 4to. Giessen und 

 Darmstadt, 1800 " (Brit. Assoc. Report, p. 35). 



There are no doubt many other tables having as much claim 

 to be included in the preceding list as some of those mentioned, 

 but it is probable that the list contains all the more important 

 factor tables and lists of primes published previous to 1811 \ 



It may be remarked that a table showing all the prime factors 

 of a number usually gives also their powers, ex. gr. opposite 4,932 

 we should find 21 3^ 137 ; but in some tables only the prime 

 factors, without the powers, are given. On account of the spaces, 

 in which the factors of each number are contained, being neces- 

 sarily of uniform size, it is not possible in many cases to give all 

 the factors at length : thus to save room in Vega's table, a, b, c, d 

 are printed for 11, 13, 17, 19, and in Lambert's Supplementa (1798) 

 /, g,...z, A,...Q are printed for 11, 13,. ..89, 97.. .173. See § 11. 



In a letter printed in his Deutscher Gelehrter Briefwechsel, t. v. 



1 Report of the forty-third meeting of the British Association, 1873, pp. 1 — 175. 

 Art. 8. Tables of Divisors (Factor Tables) and Tables of Primes, pp. 34 — 39. 



2 jt (Joes not seem worth while to continue the list of the smaller tables beyond 

 1811 : some are referred to in the British Association Report. Perhaps of the 

 small tables, that contained in the original edition (1814) of Barlow's Mathematical 

 Tables which gives prime factors and their powers for numbers to 10,000, is the 

 most convenient and accessible. The column containing this table is omitted iu 

 the later (stereotype) editions. 



