ON MATHEMATICAL TABLES. 



303 



Report of the Committee, consisting of Professor Cayley, F.R.S., 

 Professor Gr. Gr. Stokes, F.R.S., Professor H. J. S. Smith, F.R.S., 

 Professor Sir William Thomson, F.R.S., Mr. James Glaisher, 

 F.R.S., and Mr. J. W. L. GtLAisher, F.R.S. (Secretary), on 

 Mathematical Tables. 



I. The Factor Table for the Sixth Million. 



In last year's report it was stated that tlie factor tables for the fourth 

 and fifth millions had been published by Mr. James Glaisher, and that 

 the factor table for the sixth million was in the press. The printino- 

 and stereotyping of this million, the last of the three millions interven- 

 ing between the tables of Burckhardt and Dase, has been completed; 

 and the volume will be published shortly. 



II. Results of the Enumeration of the Primes in the Sixth Million. 



The following table contains the chief results of the enumeration of 

 the primes in the sixth million, arranged according to the numbers of 

 primes in the centuries. 



5,000,000 to 6,000,000. 



This table shows the number of centuries in each group of 100,000, 

 each of which contains no prime, each of which contains one prime, two 

 primes, &c. For example, between 5,000,000 and 5,100,000, there is no 

 century containing no pi'ime (i.e. consisting wholly of composite num- 

 bers), there are three centuries which contain one prime, fourteen which 

 contain two primes, &c., and so on. The number at the foot of each 

 column is the total number of primes in the group of numbers to which 

 the column relates ; thus, for example, there are 6,458 primes between 

 5,000,000 and 5,100,000. 



The corresponding tables for the fourth and fifth millions were given 

 on pp. 47 and 32 of the Eeports for 1879 and 1880 respectively. 



