Question

show that there is infinitely many positive primes

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Answer 1

Answer:

If possible, let there be finite number of positive primes p 1 , p 2 , , p n {p}_{1},{p}_{2},,{p}_{n} p1,p2,,pnSuch that. ... Clearly p 1 p 2 p n {p}_{1}{p}_{2}{p}_{n} p1p2pn is divisible by each of. < p n { p }_{ 1 },{ p }_{ 2 },{ p }_{ 3

Don't report my answers I am not fool ok

Answer 2

Given : Prime number

To Find  : Show that there are infinitely many positive primes.

Solution:

Let say there are finite prime numbers

P₁ , P₂ , . .   .  , Pₙ

x = 1 +  P₁ P₂. . .   .  .Pₙ

P₁ P₂. . .   .  .Pₙ  is divisible by all primes P₁ , P₂ , . .   .  , Pₙ

hence x = 1 +  P₁ P₂. . .   .  .Pₙ  is not divisible by any of P₁ , P₂ , . .   .  , Pₙ

=>  x is a prime number

or x has prime divisor other than P₁ , P₂ , . .   .  , Pₙ

This contradicts our assumptions

Hence we can sat prime numbers are not finite

and there  are infinitely many positive primes

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