What is the term used for a "factorial" of prime numbers ? Is there such a definition? A "factorial" of a given number $n$ is defined as a product of positive integers up to that number. What is the term used if those positive integers are prime numbers? Is there a term for that (like a product of primes or a factorial of primes)?
For example if I calculate the product of first five primes it would be $2 \cdot 3\cdot 5\cdot 7\cdot 11= 2310$. What do I call $2310$ as? Should I simply call it : "product of first $n$ primes from up to 11" or "factorial of primes up to $11$" ?

The term you are looking for is, fittingly enough, primorial. The product of the primes up to $p_n$ (the first $n$ primes) is typically denoted $p_n\#$.
