Euclid says not.
"Theorem: There are infinitely many prime numbers.

Proof:
Suppose the opposite, that is, that there are a finite number of prime numbers. Call them p1, p2, p3, p4,....,pn. Now consider the number

(p1*p2*p3*...*pn)+1

Every prime number, when divided into this number, leaves a remainder of one. So this number has no prime factors (remember, by assumption, it's not prime itself). This is a contradiction. Thus there must, in fact, be infinitely many primes."
Source(s):
http://mathforum.org/isaac/problems/prime1.html

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