Let 
be the 
th prime, then the primorial
(which is the analog of the usual factorial for prime
numbers) is defined by
 |
(1)
|
The values of 
for 
, 2, ..., are 2, 6, 30, 210, 2310,
30030, 510510, ... (OEIS A002110).
It is sometimes convenient to define the primorial 
for values other than just the primes, in which case it is
taken to be given by the product of all primes less than or equal to 
, i.e.,
 |
(2)
|
where 
is the prime
counting function. For 
,
2, ..., the first few values of 
are 1, 2, 6, 6, 30, 30, 210, 210, 210, 210, 2310, ... (OEIS
A034386).
The logarithm of 
is closely related to the Chebyshev function 
, and a trivial rearrangement
of the limit
 |
(3)
|
gives
 |
(4)
|
(Ruiz 1997; Finch 2003, p. 14; Pruitt), where e is the usual base of the natural logarithm.
