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Prove that there are infinitely many positive primes

Posted by Daksh Chattha 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 8 months ago

For any finite set of primes {p₁ , p₂ , p₃ ,......., p_n }, Euclid considered the number

n = p₁ * p₂ * p₃ *.......* p_n + 1

n has a prime divisor p(every integer has at least one prime divisor). But p is not equal to

any of the p_i .(If p were equal to any of the p_i , then p would have to divide 1, which is

impossible.

So for any finite set of prime numbers, it is possible to find another prime that is not in

that set.

In other words, a finite set of primes cannot be the collection of all prime numbers.

Hence, there are infinitely many positive primes.

0Thank You

ANSWER

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Posted by Kanika . 2 months, 3 weeks ago

CBSE > Class 10 > Mathematics