Question

Suppose n = pq where p and q is a twin prime pair (i.e. they dier by 2). Explain how this
information can help us factor n quickly. Use your method to factor 52012943.

Answer 1

twin prime..
q = p+2

Answer 2

n = (p)(p+2)=p^2+2p
p^2+2p-n=0
find p by quadratic

Answer 3

I tried but the values i got for p were not prime

Answer 4

\[
p=\frac{-2\pm\sqrt{4+4(52012943)}}{2}\\
p=\frac{-2\pm2\sqrt{1+(52012943)}}{2}\\
p=-1\pm\sqrt{52012944}\quad=-1+7212,\quad-1-7212
\]
reject the -ve

Answer 5

thanks
btw how do you put the root sign