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  • Similarly, the Greeks did not conclude that there exists no largest prime number by counting forever; they noticed that if N is a largest prime number and a,b,c,...,N is a list of all the primes then the number (a*b*c*...*N) + 1 is either a prime itself (a contradiction, since N was assumed to be our largest prime) or this number is not divisible by any of our finitely many primes, and that too is
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