gcd(3^n-2,2^n-3)

[Max]

There is a problem about values of gcd(3^n-2,2^n-3) discussed at http://www.mathlinks.ro/Forum/viewtopic.php?t=30489

I think it can give rise to a number of interesting (and hard-to-compute) sequences currently missed in OEIS.
E.g.:
1) possible values of gcd(3^n-2,2^n-3)
2) primes dividing gcd(3^n-2,2^n-3)
3) primes dividing 2^(n^2)-1
4) primes dividing 3^(n^2)-1
Remark: I think 2) is a subset of the intersection of 3) and 4) (or maybe they are equal?).
etc.

Is anybody isterested in computing and submitting these sequences?

Max