ON MATHEMATICAL TABLES. 



309 



Tcstigfition of the theory, by means whereof all but two of the pairs of inrni- 

 bcrs are obtained. The first pair is the above-mentioned one, 2'-. 5. 11 and 

 2\ 71(=220 and 284), and the fifty-ninth the high numbers 



3^ 72. 13 . 19 . 53 . 0959 and 3^ 7". 13 . 19 . 179 . 2087. 

 The hist two pairs are referred to as "formge divcrssc a precedentibus ; " viz. 

 these are 



r2M9.41 _„., r 2^41.467 



2M99 



and 



2\ 19 . 233. 



12. A Table of the Frequency of Primes is given 



Gauss, Tafel der Frequenz de Primzahlen, Werke, t. xi. pp. 436-443 ; 

 viz. this extends to' 3,000,000. 



The first part, extending to 1,000,000, =1000 thousand, shows how many 

 primes there are in each thousand : a specimen is 



viz. in the first thousand there are 168 primes, in the second thousand 135 

 primes, and so on. 



For the second and third millions the frequency is given for each ten thou- 

 sand : a specimen is 



1,000,000 to 1,100,000. 



1 



4 



12 



54 



114 



171 



217 



164 



126 



71 



39 



12 



6 



7210 





= 7212-99. 



