Server down?

[jMcCranie]

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...

OK, so how about: no double checking to try to resolve the conjecture nearly twice as quickly, but if and when it gets down to only one k with unknown status, run a double check on those.

----Added----

I'll make an analogy. Suppose that there are a large number of boxes. A small number of boxes contain a diamond and you want to find diamonds. The first time you look in a specific box, if it contains a diamond, there is a 5% chance that you will not see it.

Should you (1) spend half of your time double-checking boxes you have already opened, or (2) open as many boxes as you can? I would open as many boxes as I can.