Primorial
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.
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asymptotes (2x^3 + 4x^2 - 9)/(3 - x^2)
