More optimal method to find arbitrarily prime gaps? I was reading wolfram article about prime gaps(< and i thought that the method for finding arbitrarily large prime gaps is improvable. $$\text{If }p_i, p_2,p_3....p_k \text{are all the primes less than or equal than n, then if}\\\ m=\prod_{k=1}^{k=n+1}p_k\\\ \text{all numbers from m+2 to m+n will be composite}\\\ $$ My question is more about why don't they include this as a prime-gap generating algorithm, because I think that more than one have thought about this, and that m will be much lower than (n+1)!, therefore generating much lower bounds.

That is the way they demonstrate the existence of arbitrarily long prime gaps on the Wikipedia page.

I would guess MathWorld uses $n!$ because it is slightly easier to understand and because both approaches give bounds that are very weak.