With the mix of exponentially decreasing prime density and exponentially increasing computation times I guess the project will still be running in 2040. The question is, what'll be first, the next Mersenne prime or the next k eliminated from Five or Bust?
Another project with a chance of finding a 10,000,000+ digit prime is the generalized fermat search at Primegrid. b^2^21 has a leading edge b of 703,000, i.e. more than 12,000,000 digits. Not to mention the b^2^22 search with b of around 940,000 that  with more than 25,000,000 digits  would yield the largest known prime if successfull. That's a big if though.
