Question

Please prove prime numbers are infinite.​

Answer 1

Let's assume there are n prime nos be a1,a2.....an

here u should know that 1 is not divisible by any prime no as 1 itself is not prime

So take P = a1a2a3....an + 1

Here As P is product of many primes

So it can't be Prime

So its non prime

now if its non prime then it must be divisible by any prime a1,a2....an

Now As P= a1a2....an +1

If its divisible by any prime then 1 also should be divisible by any prime

As 1 is not divisible by any prime

So Prime nos are not finite

Its infinite

Now if its non prime