# Function Repository Resource:

# Primorial

Evaluate the primorial

Contributed by: Sander Huisman
 ResourceFunction["Primorial"][n] calculates the product of the primes up to n.

## Details

Integer mathematical function, suitable for both symbolic and numerical manipulation.
For n1, the primorial is equal to 1.
For n2, the primorial is defined as , where pk is the kth prime and π(n) is PrimePi[n].
ResourceFunction["Primorial"] has the attribute Listable.

## Examples

### Basic Examples (2)

Compute the 23# primorial:

 In:= Out= Compute a list of the first 15 primorials:

 In:= Out= ### Scope (1)

For nonpositive numbers, the primorial is defined to be equal to 1:

 In:= Out= ### Properties and Relations (2)

Compare with the definition:

 In:= Out= The resource function ChebyshevTheta is the logarithm of the primorial:

 In:= Out= ### Neat Examples (3)

Evaluate the infinite primorial:

 In:= Out= In:= Out= Compare the growth rate of the primorial versus factorial:

 In:= Out= Plot the differences between the factorial and the primorial up to n:

 In:= Out= 