+18 What is the product of the smallest two prime factors of \({2}^{1024}-1\)?
+868 Using modular arithmetic, we find
2^2014 - 1 == 1 (mod 2)
2^2014 - 1 == 1 (mod 3)
2^2014 - 1 == 0 (mod 5)
2^2014 - 1 == 0 (mod 7)
So the product of the two smallest prime factors is 5*7 = 35.
