From statement 1, we can see that p must equal the 100th prime number. The range from 1 to p+1 will then include 100 prime numbers. We can find 1 and only one value of p, since we know p is prime. If we make p any smaller, we don't get 100 prime numbers in the range. If we make p any bigger, it has to be the next prime number, and then we will have 101 prime numbers in the range. Thus, statement 1 is sufficient.

From statement 2, we have a defined range. It is thus possible (though it will take a long time) to count all of the prime numbers in that range. That will give us a definite value for p, so statement 2 is sufficient.

Since both statements are sufficient, the answer is D.