I know you guys will think that it is obvious. But if you think deep, you will notice that it is not straightforward because as the number increases, the density of the prime number decreases. If the number is large enough, then we may not get any prime number after that. Moreover, for large numbers, the chances that it has a factor are more because more numbers are candidates for its factor.
There are many methods, but the one I love most is Euclid’s method. It is based on the Proof By Contradiction method.
It follows as following.
I am another CSE student