316 ON PRIME NUMBERS. 



Example IV. 

 The prime divifor being 23*. 



Then 1 ~ 23 = •0434782608695652I73913' 

 or 

 r 1 10 8 11 18 19 6 14 2 20 16 divs. 

 •0 4347826086 quots. 



22 13 15 12 5 4 17 9 21 3 7 divs. 

 1.95652173913 quots. 



1 -f- 23' = < 



Divs. added 23 23 23 23 23 23 23 23 23 23 23 

 99999999999 



Remark. — From hence it appears, if half the dividends be 

 found (and they are eafily obtained by the continual addition 

 of a few of the firft quotient figures) the remainder regularly 

 fucceed them as complements of the former. 



Obfervation. — The refult of the divifions oT an unit by the 

 prime numbers 1 1 , 31, 37, 41, &c. appears at firft fight to 

 deviate from the general law above laid down, but in fact it 

 is fubfervient to it, as will appear from the following 

 Example. 



The prime divifor being 41*. 



C 1 10 18 16 37 dividends. 



{* 



2 4 3 9 quotients. 



40 31 23 25 4 dividends, 



9 7 5 6 quotients. 



2 20 36 32 33 dividends. 



L '0 4 8 7 8 quotients. 



{39 21 5 9 8 dividends. 

 '95121 quotients. 

 C 3 30 13 7 29 dividends. 

 (.'07317 quotients. 

 ("38 11 28 34 12 dividends. 



(.'92682 quotients. 



{6 19 26 14 17 dividends. 

 '14 6 3 4 quotients. 

 | 35 22 15 27 24 dividends. 

 1*8 5 3 6 5 quotients. 

 A table of the quotients and dividends arifing from all 

 prime numbers under 1000* is nearly completed, and will be 

 at the fervice of the public whenever it mall appear fufliciently 



beneficial. 



SCIENTIFIC 



