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What is the product of the smallest two prime factors of \({2}^{1024}-1\)?

eramsby1O1O · Answer 1 · 2024-08-14T12:29:14

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.