Do you know a polynomial $P(x)$ generating primorials, when $x=0,1,2\ldots ,M$? Just a recreational problem, that I've thought. 
For integers $k\geq 1$ let $p_k$ the $kth$ prime number, and with $$N_m=\prod_{k=1}^m p_k$$ we denote the primorial of order $m$.
This MathWorld tell us an example due to Euler of a polynomial generating only primes.

Question. Do you know or can show an example of a polynomial $P(x)$ generating only primorials for consecutive integers $0\leq x\leq M$, with $M$ for example $9\,$? Many thanks.

If you find an example with $M=19$ also you can add it, but only is required an anser of the previous question. If you develop some special algorithm to find those polynomials add some detail, please.
If you know that such exercise was in the literature you can refer it.
 A: Other answers and comments have shown how to make a polynomial of sufficient degree that produces only primorial values; I want to note that the equivalent of the "Euler result" — a polynomial such that it takes on a number of primorial values (much) larger than its degree — is impossible for a technical reason: the primorials simply aren't dense enough.
More specifically: $N_m$, the product of the first $m$ primes, grows as roughly $m^m$ (see https://oeis.org/A002110 ). But a degree-$d$ polynomial can only grow as $m^d$, so once we have $m\gg d$ the values of the polynomial will of necessity not be able to 'keep up with' primorials.
(This leaves open the possibility that, for instance, one could have a polynomial with for instance $p(1)=N_3$, say, $p(2) = N_{20}$, and then $p(3),\ldots$ 'filling in the gaps'. But even in such a case, it's possible to show that only a small number of primorials larger than the largest explicitly-specified value can be obtained before the first non-primorial value must appear.)
A: Lagrange interpolation yields
$$ {\frac {1192918183\,{x}^{9}}{90720}}-{\frac {4732108061\,{x}^{8}}{
10080}}+{\frac {106913886451\,{x}^{7}}{15120}}-{\frac {14018251313\,{x
}^{6}}{240}}+{\frac {248593167287\,{x}^{5}}{864}}-{\frac {412373959049
\,{x}^{4}}{480}}+{\frac {17052726025753\,{x}^{3}}{11340}}-{\frac {
3507552477271\,{x}^{2}}{2520}}+{\frac {322120060873\,x}{630}}+2
$$
giving the first $10$ primorials for $n=0\ldots 9$.
