Is there a biggest prime number and if yes no why?

Answer 1

No because the amount of numbers is infinite and there is no pattern to suggest that the amount of prime numbers is not infinite.

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In fact, there is a relatively simple proof that there is no biggest prime.

Suppose P were the biggest prime.

Multiply together all the primes from 2 upto P. Call this number Q.

Add 1 so that your final number is Q+1.

Now, divide Q+1 by any prime. The prime will go into Q (by the way Q is defined) and so, when dividing Q+1, there will be a remainder of 1. So Q+1 cannot be divided by any prime fro 2 to P so Q+1 is itself a prime. And the way in which it was defined Q+1 is MUCH bigger than P.