Are there more prime numbers than composite numbers?

Once you count past 10 the number of primes is less than half the total number. This implies that composites outnumber the primes.

Although prime numbers go on without limit, they becomes increasingly 'thinned out' -- the density of primes decreases as numbers get larger. There's a huge body of work on this.

When you ask about which of two infinite sets contains 'more', it gets a little dicey. Both sets are countable, i.e., aleph-null, so in that sense they are the same 'size' infinities (see transfinite numbers).

How would you answer the question, "Which is more plentiful -- multiples of 5 or non-multiples of 5 ?" Here we're talking about only 20% of all numbers -- a clear minority -- yet still an infinite set.

As there are an infinite number of each, one can not say that there are more of one than there are of the other. Infinity is infinity.

No. No prime number can be a multiple of two. Consequently, at most half +1 of all positive integers greater than 1 are prime. However, 9 is not a prime number, and neither is 35, and neither are multiples of 2, so we now know that at most half - 1 of all positive integers are prime, so there are more composite numbers than prime numbers.

no. it's easy to have many numbers in composite numbers though there can only be two numbers in a prime one.

As many have said, the answer is infinite, however the point I think you are getting at is that if you have a set of numbers reaching to "n", are there more primes or more composites in that set? The answer is composites. Primes occur much less frequently than composites and become less and less frequent the higher up you go.

There are more composite numbers. The reason for this is simple

Between negative infinity and positive infinity, there are an equal amount of odd and even numbers. All even numbers are composite (they can be divided by 2). All I need then is to prove that at least one odd number is also composite. 51 is odd and is composite because 17x3 = 51. So all even numbers and at least one odd number are composite. Therefore, more composites exist than primes.

There are an infinite number of prime numbers and an infinite number of composite numbers. You cannot say that one infinity is more then another so technically speaking there is the same number of prime numbers as there are composite numbers.