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'suppose that p
1=2 < p
2=3 < ... < p
r are all of the primes. Let P = p
1*p
2*p
3...p
r+1 and let p be a prime dividing P; then p can not be any of p
1, p
2, ..., p
r, otherwise p would divide the difference P-p
1*p
2*p
3...p
r = 1, which is impossible. So this prime p is still another prime, and p
1, p
2, ..., p
r would not be all of the primes', Euclid, 300 BC