3,756,801,695,685 x 2 ^666,669 ^=to the power of
(the largest known prime)
OR
(10^87 -1)! ^=to the power of
(The number of connections among all the particles in the observable universe)
If it is the case that the number of connections connecting every particle to every other particle is far greater than the largest currently-known prime, there are nonetheless an infinite number of primes larger than it (because the primes are infinite and the number of connections is finite).
It looks like the OP meant the exponent of the first number to be the largest known prime, in which case he forgot the -1 (largest known primes are always of the form (2^n -1) ). But that’s an out of date value; the current largest known prime is 2^77,232,917 − 1