TRANSACTIONS OF THE SECTIONS. 



21 



A preliminary account of the whole enumeration is published in the 'Proceedings 

 of the Cambridge Philosophical Society/ vol. iii. pp. 17-23,47-50 (1876 and 1877). 

 Calling, for convenience of expression, the hundred numbers between 100rt-l and 

 100 (»+l) the (n + l)th century, then the enumeration was made by centimes — 

 that is to say, the number of primes in each century was obtained by counting, and 

 entered in its proper place upon a printed form. The results were then classified in 

 tables ; and those published in the Cambridge Phil. Soc. Proc. give the number of 

 centimes, in each group of 100,000 in the six millions, which contain n primes, 

 for n as argument. Thus, for example, the eighth column of the table for the third 

 million shows that in the thousand centimes between 2,700,000 and 2,800,000 there 

 is no century that contains no prime ; 2 centuries, each of which contains one prime ; 

 7 centimes, each of which contains two primes ; and so on, there being 195 centimes 

 containing .six primes and one containing seventeen primes. 



The following is a similar Table, in which each column has reference to a 

 million : — 



The number of primes in the first million has been obtained by Meissel ('Mathe- 

 matische Annalen,' t. ii. 1870, pp. 030-642), and his results agree with my own. 



* 1 and 2 are both counted as primes. 



