Mmmmm....let's see
2^1024 - 1 =
(2^512 + 1) ( 2^512 - 1)
And
(2^512 - 1) = ( 2^256 + 1) (2^256 - 1)
And
(2^256 - 1) = (2^128 + 1)(2^128 - 1)
So we see that the pattern of the smaller factors is
(2^64 - 1)
(2^32 - 1)
(2^16 - 1)
(2^8 - 1)
(2^4 - 1) = (2^2 + 1) ( 2^2 - 1) = (5) (3)
(2^2 - 1) = (2 + 1) (2 - 1) = (3) (1) 1 is not a prime
So....the smallest prime factors = 3 , 5
Their product =15