There are an infinite number of prime numbers. If you take a bunch of prime numbers and multiply them by each other and add 1 you will get a prime number (2*3+1=7, 2*3*5+1=31). So therefore if, theoretically, there was a finite amount of primes (p1, p2, p3,… pn), and you multiplied them all by each other and added one (p1*p2*p3…*pn+1) you would get a new one so therefore it must be infinite.
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