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2 and 3 are consecutive prime numbers; therefore, such a concept does exist, but those are the only two consecutive primes. The reason there are not any others: natural numbers alternate between odd and even numbers. When the number is even, then 2 is a factor. The number 2 is the only even Prime number (it's only factors are 2 and 1). All other even numbers have factors, in addition to 2 & 1. So if a number is prime, and the number is not 2, then it is an odd number. The two numbers on either side of an odd number are even. So if the prime number is greater than 3, then the two numbers on either side of it will be even numbers, which are not primes.

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Q: Why is that there are no consecutive prime numbers?
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