Is there a rule for prime numbers?

It depends on what you mean by "formula". Certainly no formula is known such that using it to find a new very large prime would be "very simple".

As you already mention yourself: it doesn't make sense to keep on looking for prime numbers with computer algorithms if there is a prime number equation.

Looking at the formulas on the site you provided, it seems to me that the formulas are really just an algorithm which allows you to determine whether some number is a prime number based on the previously found prime numbers. That I could already do in highschool by just checking whether a number can be divided by the previous prime numbers with integer solution (larger then 1). Probably, I cannot judge that quickly, the algorithm is more efficient then what I mention, but it still not a 'plug in the numbers and have your answer with a pocket calculator'.