Show that number of primes is infinite.

If possible, let the number of prime numbers be finite and equal to n.
Now according to the order of increasing magnitude.

Let the prime number be  P1, P2, P3,...........Pn

Let K=P1.P2.P3...........Pn
Now, none of the P's is a division of (K+1)
Therefore,(K+1) is either a prime  > Pn or has a prime (>Pn) as a divisor.

But this contradicts our assumption, namely Pn is the greatest prime number.

Hence numbers of primes are infinite.

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