Assume that p3 = p1 + p2 / 2 is a prime number for some consecutive p1, p2. Since p3 is the mean of p1 and p2, p1 < p3 < p2. This is a contradiction to p1 and p2 being consecutive prime numbers. Therefore, the mean of p1 and p2 cannot be a prime number.
Any prime number is an odd number so if p1 is odd the consecutive number p1+1 will be even which contradicts p2 to be prime. Hence its not possible.
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