Prime exponential k-function: a task about the symmetry of numbers

Let f_k(x,y,z,t) =2^x+3^y+5^z+7^t, x,y,z,t \in N, where k=4 and defines the number of consecutive primes used for the function, i.e. here: {2,3,5,7}. For all prime p find all such (x,y,z,t) such that f(x,y,z,t)=p (if exists).

Additional question: how does that change when f_2(x,y)=2^x+3^y (and the rest of the task changes accordingly)?

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