Inspired by Calvin and Steven.
True or False:
Considering the set of positive integers , since every odd number is followed by an even number and vice-versa, therefore there can be no two consecutive prime numbers .
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1 solution
The error that most people often commit is to think that every even natural number must be a composite number, since all numbers have the number itself and 1 as a factor (which make up for two factors) and there is a necessity of just one more factor to make them composite, in this case, we have the number 2.
However , the number 2 itself is such an even number that it has only two factors, 1 and itself. Thus, the statement posed in the problem is correct for the fact that
But it is not true that
The only counterexample is this case is the prime pair ( 2 , 3 ) .