Prove that infinitely many prime numbers are possible.
Solution Scheme and approach
Let if possible there are a1,a2...an number of finite primes.
Consider another number
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.