Euclid

Proof. Suppose that p1=2 < p2 = 3 < ... < pr are all of the primes. Let P = p1p2...pr+1 and let p be a prime dividing P; then p can not be any of p1, p2, ..., pr, otherwise p would divide the difference P-p1p2...pr=1, which is impossible. So this prime p is … Continue reading “Euclid”

Proof. Suppose that p1=2 < p2 = 3 < ... < pr are all of the primes. Let P = p1p2...pr+1 and let p be a prime dividing P; then p can not be any of p1, p2, ..., pr, otherwise p would divide the difference P-p1p2...pr=1, which is impossible. So this prime p is still another prime, and p1, p2, ..., pr would not be all of the primes. (Ribenboim's statement of Euclid's proof)

2 thoughts on “Euclid”

  1. Over my head. You need to start a separate blog called,” My Small Ship” for famous mathematical quotes.

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