a prime pair is a pair of prime numbers whose difference is 2, such as 3 and 5, or 11 and 13. Mathematicians have tried in vain to answer the question whether there are infinitely many such pairs, or only a finite number of them. It is not even known whether this question is computable. Let us suppose that it is not. That is to say that no one, and no computer, can ever produce a proof either that there are only finitely many prime pairs or that there are infinitely many. Even so, the question does have an answer: one can say with certainty that either there is a highest prime pair or there
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