Prime factorization of integers Find the prime factorization of the following integers:
$e) 2^{30} -1$
Click here for the solutions
I used the formulas: 
$a^2-1^2=(a-1)(a+1)$
$a^3+b^3=(a+b)(a^2-ab+b^2)$
$a^3-b^3=(a-b)(a^2+ab+b^2)$
And I became:
$2^{30} -1$
$=(2^{15}-1)(2^{15}+1)$
$=(2^5-1)(2^{10}+2^5+1)(2^5+1)(2^{10}-2^5+1)$
$=31*1057*32*993$
$=2^5*3*7*31*151*331$
What did I do wrong?

the trick in c) to transform $2^{15}$ in $(2^5)^3$ and use $a^3-b^3$ formula
