10:01 AM
Twin prime project : Given a prime numer $p$ , find the smallest prime number $q>p$ such that $p$#$\cdot q\pm 1$ is a twin prime pair, if such a prime $q$ exists. I found a pair for all primes below $1000$.

1 hour later…
11:19 AM
@MrPie Substitute $b=a\tan v$
@MrPie You have to be careful with this substitution. What is the domain of $u$? Is it $\Bbb R$ or something else? When you have $(b^2-a^2)/(b^2+a^2)=1-2a^2/(b^2+a^2)$ the range is $[-1,1]$ so anything outside that interval won't be defined.