48 



REPOET 1879. 



been published in the ' Proceedings of the Cambridge Philosophical 

 Society,' vol. iii. pp. 20-23, 54-56 (1877). 



It may be remarked that in the first million there is no century con- 

 sisting wholly of composite numbers, in the second there is one, in the 

 third one, in the fourth two, in the seventh six, in the eighth four, and in 

 the ninth four. 



It will be seen from the above table that no century in the fourth 

 million contains more than fourteen primes, and that only four contain 

 this number. In the third million, however, there is one century con- 

 taining as many as seventeen primes, one containing fifteen, and no less 

 than six containing fourteen ; in the seventh million there are three con- 

 taining fourteen primes, in the eighth million two containing fourteen, as 

 well as two containing fifteen, and in the ninth million two containing 

 fourteen. 



The next table shows the number of primes in each successive group 

 of ten thousand between 3,000,000 and 4,000,000. Thus, for example, 

 between 3,000,000 and 3,010,000 there are 670 primes; between 3,010,000 

 and 3,020,000 there are 659, . . . ; between 3,100,000 and 3,110,000 there 

 are 676, and so on. The numbers in the lowest line of the table are ob- 

 tained by adding the numbers in each column, and agree, of course, with 

 the numbers at the foot of the columns in the previous table. 



3,000,000 to 4,000,000. 



The numbers of primes in each of the seven millions are :- 



First million 

 Second „ 

 Third „ 

 Fourth „ 



Seventh „ 

 Eighth „ 

 Ninth „ 



Number of 

 Primes 



78,499' 

 70,433 

 67,885 

 66,329 



63,799 

 63,158 



62,760 



Difference 



8066 

 2548 

 1556 



641 



398 



1 1 and 2 are'eounted as primes. 



