By the measure of cardinality, which it is most conventional to use when measuring infinite sets, there are the same number of prime numbers as there are integers. This measure is defined by being able to place the sets in bijection which means you can place them into 1:1 correspondence and never have either a prime left over with no corresponding natural number, nor can you have a natural number left over with no corresponding prime.
However there are those who would argue that identity is a stronger measure of correspondence than bijection. And by this argument we can see that the prime numbers are a proper subset of the integers and therefore no matter how many prime numbers we might count, every single one will not just be in $1:1$ correspondence with an integer, it it will actually be an integer, and will be in the set of integers. The set of integers contains all of those and all of the compound numbers on top.
This second measure is best captured by the notion of density. We can say that the integers have density $1$ in themselves while the prime numbers have a density lower than $1$ among the integers.
Cardinality is useful when we need to compare sizes of infinite sets and we're unable to compare them by the identities of the elements within, which is frequently the case.
If trees continue producing apples and oranges for eternity, density will correctly measure the fact that the fruit basket would need to be bigger if you planned to pick both types of fruits. Cardinality on the other hand would simply tell you that you need a really big basket either way.