$$2^{2176}\cdot 3^{2175}\pm1$$ is an example of a twin-prime pair of the form $$2^a\cdot 3^b\pm 1$$ with positive integers $a,b$. Each prime "only" has $\ 1\ 693\ $ digits, so larger examples probably exist.
Have such twin-primes be searched upto a high range ? If yes, what is the largest known twin-prime of this form ?
Update : Enzo Creti found the twin-prime $$2^{5211}\cdot 3^{5794}\pm1$$ with $4\ 334$ digits each.