Evaluate the primorial of a number

J, 13 characters

*/p:i._1 p:1+

Examples:

   */p:i._1 p:1+7
210

   */p:i._1 p:1+12
2310

Python 2, 49 bytes

P=k=1
exec"P*=P**k%k<1or k;k+=1;"*input()
print P

Counts up k from 1 to the input, updating the primorial P by multiplying P by k whenever it's prime. Since P contains all lower prime factors, a sufficiently high power of P will contain k as a factor if and only if k is non-prime. The power P**k suffices, and we check whether P**k%k<1, multipling P by 1 if so (doing nothing) and by k otherwise.

Python, 72 characters

Quickly golfed, I imagine there are better python solutions.

n=t=1;exec"t*=(1,n)[all(n%i for i in range(2,n))];n+=1;"*input();print t

I used wikipedia to verify up to 71

Usage:

$ python primorial.py
100
2305567963945518424753102147331756070

$ python primorial.py
101
232862364358497360900063316880507363070