Happy new year.

I am studying the product of consecutive prime numbers. For the $n$-th prime number $p_n$, I denote $\mu_{n}=p_1 p_2 \ldots p_n$.

The problem is that I can not search for the properties of $\mu_{n}$.

Thus, I'd like to know some properties about the $\mu_{n}$. It does not have to have detail. I wonder just name of theorem or related some paper.


  • 2
    $\begingroup$ Welcome to Mathematics Stack Exchange. Cf. primorials, denoted $p_n\#$ $\endgroup$ – J. W. Tanner Dec 31 '19 at 13:14
  • $\begingroup$ Oh! really thank for help. Happy new year! $\endgroup$ – himath Dec 31 '19 at 13:17

The product of the first $n$ primes is called primorial and denoted $p_n\#$.

You can read more about them on Wikipedia or MathWorld.

  • $\begingroup$ Thanks! It is enough. I'd like to close the question. $\endgroup$ – himath Dec 31 '19 at 13:29
  • $\begingroup$ @Giyuob Don't close the question. Leave it up for others to use. $\endgroup$ – Ethan Bolker Dec 31 '19 at 13:55
  • $\begingroup$ @Giyuob: thank you for accepting my answer; best wishes $\endgroup$ – J. W. Tanner Dec 31 '19 at 14:00
  • $\begingroup$ Okay! I'll leave it. I'm sorry, I did't know mean that closing. $\endgroup$ – himath Dec 31 '19 at 14:02

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