Natural Number: the counting numbers:
1, 2, 3 ,4, 5...
Prime Number: natural number who's only natural number factors are 1 and itself:
1, 2, 3, 5, 7...
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Technically no, because all numbers are infinite, and no infinity is less or more than another. It depends on how you view "more." If you speak of the natural numbers and prime numbers increasing at a constant rate relative to one another, then there will be "more" natural numbers.