34 



EEPOBT — 1880. 



III. Results of the Enumeration of the Primes in the first Five Millions. 



The following table is similar in form to the first table of Section II. ; 

 each colnmn relates to a million numbers, and the last column to the 

 ■whole five millions. The last column but one, which refers to the fifth 

 million, is of course identical with the last column in the table in 

 Section II. 



to 5,000,000. 



It will be seen from this table that the centuries with eight primes are 

 the most numerous in the first million, the centuries with seven primes 

 in the second and third millions, and the centuries with six primes in the 

 fourth and fifth millions. It may be mentioned that the centuries with six 

 primes are also the most numerous in the seventh, eighth, and ninth 

 millions. 



•The 26-prime century is of course the first, namely, from to 99, and 

 the 21-prime century the second. In the first century 1 is counted as a 

 prime. 



The next table shows the number of primes in each group of 10,000 

 from to 5,000,000, with differences. For example, the number of primes 

 between and 10,000 is 9,593, between 10,000 and 20,000 is 8,392 ; 

 between 1,000,000 and 1,010,000 is 7,216 ; and so on. 



