«N PRIME NUMBERS. 315 



Example I. 



1 -2-7 = -142857 

 or 



1*7= J' 14 ? ' • '"'Half. 



f'H2 . . 1ft. 7 

 [857 . . 2d. J 



Quotient figures added m 9 9 9 



Example II. 



1 -r 29 = -6344827586206896551724137931* 

 or 



1 ~ 29 = | '03448275862068 . lft. 7 haJf 

 1 9665172413~93i . 2d. 3 



Quotient figures added 99999999999999 



Remark. — From hence it appears, that if half fuch like 

 quotients be found by divifion, the other moiety may be ob- 

 tained by a fimple addition only. 



2. The firft: half of the dividend figures (or fucceflive re- Law of the re- 

 mainders) arifing from the divifion of an unit by any prime ^" de _?_ ^ 

 number, not lefs than the number 7, will be the complements pr i me numbers. 

 oi the other half to the prime divifor. 



Example III. 

 The prime divifor being 17'. 

 Then 1 ~ 17 = -0588235294117647 



(1 10 15 14 4 6 9 5 1ft. half of div. 



f'6 588235 



•5? 17 = < 16 7 2 3 13 11 3 



1-941 1764 



5 2 lft.halfofquots. 

 3 t2 2d. half of div. 



7 





Example 



