You can't prove a negative.
If there were, call it p, and let q = Π(P), P∈N:P is prime (Eratosthenes showed this is computable)
Then q+1 % 1 modulo every lesser prime, meaning q+1 is prime, and p is thus not the greatest prime.
There you go. We have just proven a negative.
Which is maybe not the worst strategy, but it's going to be pretty exhausting.
I'd suggest that instead we should just expect and enforce a certain amount of openness and honesty from companies when they fuck up in this way, so we can make informed decisions.
In the US and elsewhere, there are already some penalties for covering up a problem, and they should be expanded commensurately with the potential harm.