Consider the highly unlikely possibility that there's only one prime for a given k. A false negative with no double checking means we crunch that k forever and never prove the conjecture. Unlikely to happen that way, but not impossible. People more in the know claim an error rate of about 4% (IIRC) on GIMPS. On the PrimeGrid message board, someone mentioned that a SOB work unit had to be sent out on average of 4.7 times to get a matching doublecheck. That post is three years old, but I can't image the situation is much different now. I still think double checking is valuable.