The primorial, a portmanteau of prime and factorial, is formally defined as \[p_n \# = \prod^{n}_{i = 1} p_i\] where \(p_n\) is the nth prime. Another slightly more complex definition, which expands the domain of the function beyond prime numbers, is \[n \# = \prod^{\pi (n)}_{i = 1} p_i\] where \(p_n\) is the nth prime and \(\pi (n)\) is the prime counting function. Using either definition, the primorial of n can be informally defined as "the product of all prime numbers up to n, inclusive." For example, \(16 \# = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 = 30030\). \[\lim_{nightarrow\infty} \sqrt[p_n]{p_n \#} = e\]