210 



Ex. IV. N=7429 



N'= 42 2=422=2-2il, 

 / 



the number N is divisible neither by 7 nor by 13. 



Remark. The above proceeding is but the application of a 

 general principle, inherent to our decadic system. The author is in 

 possession of similar proceedings for all prime numbers up to 107 ; 

 above that limit (except a few cases) the rules become more com- 

 plicated, and lose the high value of easy application. 



Taking again N=abcde . . . mn, we have the following Table for 

 operating by the different prime numbers up to 109 : 



Divisors. Operation. 



7,13 .................. d-a 



17,59 .................. d-3a 



19,53 .................. d7a 



23,43 .................. +<f 



29 .................. e 50 



31 .......... ........ + X*^1 



' ' 



+. 



41,61 .................. e4a 



w .................. -t 



67 .................. dsa 



73, 137 ................ e-a 



83 d 



83 .................. +40 



c d 



101 .................. c-a 



107 . c-7 



