ON MATHEMATICAL TABLES. 



305 



The corresponding lists of sequences for the fourth and fifth millions 

 were given on pp. 49 and 33 of the Reports for 1879 and 1880 respec- 

 tively. 



III. Results of the Enumeration of the Primes in the First Nine Millions. 



As the gap between Burckhardt's and Dase's tables is now completely 

 filled up, it is possible to give results derived from an enumeration of 

 primes extending without break over the first nine millions. 



The following table (which is similar in arrangement to th.e first 

 table in Section II.), shows the number of centuries in each of the nine 

 millions which contain no prime, one prime, &c. The number at the 

 foot of each column is the number of primes in the million. 



to 9,000,000. 



It appears 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 all 

 the other millions. 



1881. 



