20 Mr Glaisher, On the Results of an enumeration [Dec. 4. 



and the slowness with which the numbers diminish is apparent. 

 The average number of primes throughout all the three millions is 

 about 6*3 per cent. 



In Base's tables there is nothing to show whether the number 

 6,036,637 is or is not a prime. This is due to a fault in printing, 

 the space being blank through the type having slipped back. In 

 Table I, and in the numbers given above, I have assumed that 

 6,037,637 is a prime. This is, of course, merely a provisional 

 assumption, as I shall hereafter decide the question by trial, but 

 certainly the number has no very small divisor. 



It is perhaps desirable to state, although it follows from what 

 has been already said, that the numbers given in the 'primes 

 counted' column of my British Association paper, for the ninth 

 million, have all received confirmation by the recent examination 

 of this million. 



In regard to the work now in progress, I have thought it 

 safer that the new enumeration should be quite distinct from the 

 old, and accordingly it is being proceeded with entirely de novo, 

 as if the old enumeration were not in existence. For the 

 new enumeration two sets of blank forms were printed, the 

 one to contain the number of primes in each century, there being 

 places for 400 centuries (corresponding to 40,000 natural numbers) 

 on each form, which is of the size- of a somewhat large foolscap 

 page, and the other to accommodate tables similar to Tables 

 I, II, III. These are found to be a great convenience. In the 

 old enumerations all the forms were ruled by hand, and the gain 

 both in accuracy and clearness which results from the employment 

 of the printed sheets is even greater than I expected it would be. 



