No, negative prime numbers do not exist. By definition, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
When we talk about prime numbers, we are specifically referring to numbers in the set of natural numbers, which are 1, 2, 3, and so on, extending infinitely in the positive direction. Prime numbers are formed from these natural numbers, and the concept of primality relies on the number being greater than 1.
If we consider negative numbers, they fail to meet the fundamental criteria for primality because they are not part of the natural number set. For instance, the negative counterpart of a prime number, such as -2 or -3, would have the same factors as their positive counterparts, but the prime concept does not apply to them. Thus, no prime numbers exist within the realm of negative integers.