1878.] Mr Glaisher, On factor tables. 123 



contained in Chernac's description : " Adolph. Frid. Marci, vir in 

 rationibus subducendis exercitatissimus, sive sua sponte, sive lior- 

 tatu Lamberti excitatus, animum adjecit ad terminos hujusmodi 

 tabularum ampliandos. Tabellam adornavit, in qua exhibentur 

 numeri tantummodi {sic) primi in quater centenis millibus obvii. 

 Impressa esse (sic) Amstelodami, typis J. Morterre in 8. anno 1772. 

 Hoc opusculum parcius videtur innotuisse exteris, in quorum 

 diariis nusquam ejus mentionem factam reperio," {Crihrum, p. ix.) 

 In 1797 Yega published his well-known Tabulce logarithmico- 

 trigonometricce, of which vol. ii. contains a. factor table to 102,000, 

 and a list of primes from 102,000 to 400,031 \ Vega does not 

 state whence these tables were derived. He merely remarks that 

 anyone can convince himself of the accuracy of the former by 

 comparing it with Neumann's table. Both tables have been re- 

 produced, I believe, in all the editions of this valuable collection 

 of tables that have been issued. Chernac gives, a list of errors 

 in the factor table and in the list of primes on the last two pages 

 of his Crihrum (1811) ; see § 14. 



§ 14. I now come to the great factor tables that have been 

 published during the present century, viz. : 



Chernac (1811). All factors to a million. 



Burckhardt (1814 — 1817). Least factors to three millions. 



Dase (1862 — 1865). Least factors for the seventh, eighth, 

 and ninth millions. 



The title of Chernac's work is "Cribrum arithmeticum sive, 

 tabula continens numeros primos, a compositis segregates... . Nu- 

 meris compositis, per 2, 3, 5 non dividuis, adscripti sunt divisores 

 simplices, non minimi tantum, sed omnino omnes. Confecit Ladis- 

 laus Chernac... Daventrise... Anno MDCCCXI." It contains all prime 

 factors of numbers not divisible by 2, 3, or 5, from 1 to 1,020,000, 

 on 1,020 quarto pages. All the prime factors are given, ex. gr. for 

 828,443 we have 7. 7. 11. 29. 53, for 828,563 we have 17. 17. 47. 61, 

 &c. ; and the primes are distinguished by long black bars which" 

 are very distinct. There are 1,000 numbers on each page, i. e. the 

 factors of numbers between 100071 and 1000 {n + 1) are found on 

 page (ii + 1). The mode of entry is simple, and the figures are 

 clear. 



The table is exceedingly accurate. Burckhardt, who examined 

 it (see § 16), found only 38 errors ; of these 26 are due to a rule 

 having fallen out from the top of a column and been wrongly 

 replaced at the bottom : 3 others have been produced by a similar 

 accident. Of the remaining 9 one is a mere tr^ansposition of two 

 factors, 3 are errors in factors such as 13 for 23, while only 5 result 

 from real errors in the calculation. 



1 In Hiilsse's edition of Vega (1840) the list of primes extends to 400,313. 



