Is there any theoretical indication that this conjecture of Catalan could be true?

Belgian mathematician Catalan in $1876$ made next conjecture: If we consider the following sequence of Mersenne prime numbers: $2^2-1=3 , 2^3-1=7 , 2^7-1=127 , 2^{127}-1$ then $$2^{2^{127}-1}-1$$ is also prime number. The last term has more than $10^{38}$digits and cannot be tested at present, so I would like to know is there any theoretical indication that Catalan's conjecture could be true ?

EDIT:

At London Curt Noll's prime page I have found statement that this number has no prime divisors below $5*10^{51}.$

I don't know of any theoretical reason to think it would be true. I would conjecture it to be false.

Standard heuristics suggest that the first unknown example would be prime with probability $$e^\gamma\cdot2^{-120}\approx1.34\cdot10^{-34}\%$$ which is small.