Primorial
From Number
Definition
Let 
be a natural number. The 
primorial, sometimes denoted 
, is defined as the product of the first prime numbers.
The primorial 
is defined to be 
.
An alternate definition of primorial, called here the primorial of the second kind, is defined as the product of all the primes less than or equal to a given number. Note that the logarithm of the primorial of the second kind is the first Chebyshev function.
Occurrence
Initial values
The values of primorials at 
are given in the list: 1, 2, 6, 30, 210, 2310 View list on OEIS
Special properties
- The primorial is the smallest natural number
with 
, where 
is the prime divisor count function.
- Every primorial is a minimum-so-far for the ratio of the Euler phi-function and the identity function.
