Mr. C. J. Hargreave on the Law of Prime Numbers. 



Sn(-) =1,498,954 



121 



^N 



w =1,000,000 



(~) = 901,506 



SN^^-^) = 53,597 

 \pppp / 



<PPPP' 



sn(-^— ) = 



XppppppJ 



Sn(— ) = 286,846 

 \ppp/ 



Sn(-^-) = 6,106 

 \ppppp/ 



395 SN 



xppppppp/ 



1,955,498 



1,791,912 



Thus learning 163,586 as the number of numbers whose lowest 

 prime factor exceeds 23. 



Using the second process for the primes above 23, we writfe 

 down the following table in two columns ; the first contains the 

 quotients obtained by dividing x by the primes from 997 (the 

 next prime below x\) to 29, and the second contains the number 

 of primes between the divisor and the quotient. The first column 

 is obtained from a table of reciprocals, and the second column 

 from Barlow^s table of primes, where they are in efi*ect already 

 counted. 



