Prove that there are infinitely many positive primes

1.	Prove that there are infinitely many positive primes
Answer» For any finite set of primes {p1\xa0,\xa0p2\xa0,\xa0p3\xa0,.......,\xa0pn\xa0}, Euclid considered the numbern =\xa0p1\xa0\xa0p2\xa0\xa0p3\xa0.......\xa0pn\xa0+ 1n has a prime divisor p(every integer has at least one prime divisor). But p is not equal toany of the\xa0pi\xa0.(If p were equal to any of the\xa0pi\xa0, then p would have to divide 1, which isimpossible.So\xa0for\xa0any finite set of prime numbers, it is possible to find another prime that is not inthat set.In other words, a finite set of primes cannot be the collection of all prime numbers.Hence,\xa0there are infinitely many positive primes.

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