They represent the largest known primes, as the special case 2^n-1 allows us to verify their primeness using a method much more efficient than checking all pote

They represent the largest known primes, as the special case 2^n-1 allows us to verify their primeness using a method much more efficient than checking all potential factors. So to answer your question, if there's ever a need for ridiculously large numbers that are known to be prime this is how we'll fill it. Short of that need, it's still fun as a mathematical world record!