Tuesday, 24 May 2016

elementary number theory - Is there a better way to factor 375007 with out testing first 612 primes? No calculators please

Is there a better way to factor 375007 with out testing first 612 primes ?






I know this factors to 31×12097 by testing the primes 2,3,5,,31.
Is there any other clever way to work this ? I have tried Fermat's factorization by writing the number as x2y2 but it is also taking too many iterations because the factors differ by large magnitude.



Also I have been trying to factor it by changing the base to 10^2 : 37x2+50x+7=(ax+b)(cx+d) and other bases but no success yet.

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