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of that prime number be fought by the fame method as that 

 which was to be ufcd for the difcovery of the firft logarithm; 

 and no prime faftor will occur to prevent the logarithm of 

 this number from being found immediately. — For, fince, when 

 the fador x— i is taken to denote the prime number whofc 

 logarithm is fought, the other odd fador exceeds it by 2 ; and 

 when the fador x — 2 is taken to denote it, the remaining 

 odd fador exxeeds it by 4 ; if the number exceeding the given 

 one, when denoted by the fador x — i , by two, or when de- 

 noted by the fador x—2, by 4, be compofite, the logarithm 

 may be found immediately : But if, in the firft cafe, the num- 

 ber exceeding the given one by 2, be prime, the number which 

 exceeds that number by 2 (or the given one by 4) will be 

 compofite — and if in the other cafe, the number exceeding the 

 given one by 4 be prime, the number which exceeds that 

 number by 4 (or the given one by 8) will be compofite — fo 

 that the method of notation remaining unvaried, no prime fador 

 will occur to prevent the logarithm of that prime number (by 

 the intervention of which, the logarithm firft fought is to be 

 deduced) from being found immediately. 



It is eafy to fhew, that, if the number which exceeds any 



prime number greater than 3, by 2, be prime, the number 



which exceeds it by 4, will be compofite ; or, if the number 



which exceeds it by 4 be prime, that number which exceeds 



it 



