For the 1st one, its easy to see that $\displaystyle 91 = 7 * 13$ so its definitely not prime.
Also $\displaystyle 3^{90} = 1mod\ 90$ (from observation)
You can also construct a new pseudoprime N using the proposition:
Let b >= 2 (where b is the base of this pseudoprime) and p an odd prime where p does not divide b(b-1)(b+1) then
$\displaystyle N = \frac{b^p -1}{b-1}*\frac{b^p+1}{b+1}$
If someone could review this and check for correctness, that would be great!
Edit: it works fine.