I need to find a prime factor, $p$, of $1002004008016032$ such that $p \gt 250000$. Now this is a very large number and I know it would be stupid of me to factorize such a large number into its prime factors . Any help how I can solve this ?

  • 2
    $\begingroup$ $2^5\times 3^2\times 7\times 109^2\times 167\times 250501$ $\endgroup$ – polfosol Dec 31 '16 at 18:03
  • $\begingroup$ How did you figure out such nasty factors :) $\endgroup$ – user366398 Jan 1 '17 at 0:25
  • $\begingroup$ Go here $\longrightarrow$ alpertron.com.ar/ECM.HTM It is a calculator and strictly works for integers. When a decimal is put, it will round the result to the nearest integer. When given an equation or inequality, it will return $-1$ if true and $0$ if false. It also has many other functions you can learn :) $\endgroup$ – Feeds Mar 30 '18 at 18:26


Taking $x=10^3,y=2$, we get



$\frac{x^6-y^6}{x-y} = (x+y)(x^2+xy+y^2)(x^2-xy+y^2)$

=$1002\times1002004\times998004 = 1002\times16\times250501\times249501$

Hence, the prime number , $p\gt250000$ is $250501$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.