Yes. To prove this, we must first assume the answer to be no. If there are a finite number of primes, there must be a largest prime. We'll call this Prime number n. n! is n*(n-1)*(n-2)*...*3*2*1. n!, therefore, is divisible by all numbers smaller than or equal to n. It follows, then that n!+1 is divisible by none of them, except for 1. There are two possibilities: n!+1 is divisible by prime numbers between n and n!, or it is itself prime. Either way, we have proved that there are prime numbers greater than n, contradicting our initial assumption that primes are finite, proving that the number of primes is infinite.
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Since there are an infinite number of prime numbers, there are infinite numbers with any given number of prime factors.
No, there are an infinite amount of non-prime numbers just as there are an infinite number of prime numbers.
There are more than 25 prime numbers; there are an infinite number of prime numbers.
There is an infinite number of prime numbers. It is not possible to list them.
The prime numbers after 200 are infinite. The next prime number after 200 is 211.