1877.] of the Primes in BurcJchardt' s Tables, 53 



explains a process of calculating the number of primes up to any 

 limit, whicli applied to the first million gives 78,494 as the number 

 of primes. A determination is also given of the number of primes 

 in the first ten millions. 



In two copies of Burckhardt's Tables (and therefore very likely 

 in all) there is no mark whatever to be seen corresponding to the 

 number 2,882,699: this is no doubt caused by the type having 

 slipped back. On commencing the investigation of whether this 

 number was or was not a prime, it at once appeared that it was 

 divisible by 19. 



In Table I of my previous paper it was assumed that 

 6,036,637 ^ was prime. This is correct. I have had the number 

 divided by all the primes up to 2,457 by two computers inde- 

 pendently, and have compared the separate divisions : in all cases 

 there was a remainder. 



In this preliminary account I have confined myself entirely to 

 the chief results of the enumeration, and have given no compari- 

 sons with the lia? formula. A good many values of the integral 

 are already calculated, but it seems desirable to reserve any 

 discussion of the agreement between the primes counted and the 

 formulae till the comparisons can be given in a complete form. 



1 This nnmber is correctly given in line 5 of p. 20, but in line 8 it is misprinted 

 6,037,637. Also, in line 6 of p. 18, t. ni, should be t. ii. 



