**#Problem 10**

Prove that infinitely many prime numbers are possible.

Solution Scheme and approach

Solution Scheme and approach

Let if possible there are a1,a2...an number of finite primes.

Consider another number

N=(a1*a2*a3*...*an)+1

Now we can say,

N is such a number which can be divide by all primes but always gives a remainder 1. Hence, contradiction.

Because any number>1 should be divisible by at least one prime number.

=>Infinite primes are possible. Q.E.D.

=>Infinite primes are possible. Q.E.D.

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