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

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

Thank you Cphill