Gardner riddle on mathemagicians

The Grand Master top-scores with a mere $3^2 \times 5^2 \times 7^2 \times 11 = 121275$ and the other scores are: $$\begin{array}{|c|c|} \hline \text{Disciple} & \text{Score} & \text{Composition} \\ \hline 1 & 80850 & 3 \times 5 \times 5 \times 7 \times 7 \times 11 \times 2 \\ \hline 2 & 53900 & 5 \times 5 \times 7 \times 7 \times 11 \times 2 \times 2 \\ \hline 3 & 32340 & 5 \times 7 \times 7 \times 11 \times 2 \times 2 \times 3 \\ \hline 4 & 19404 & 7 \times 7 \times 11 \times 2 \times 2 \times 3 \times 3 \\ \hline 5 & 13860 & 7 \times 11 \times 2 \times 2 \times 3 \times 3 \times 5 \\ \hline 6 & 9900 & 11 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 \\ \hline 7 & 6300 & 2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 7 \\ \hline 8 & 22050 & 2 \times 3 \times 3 \times 5 \times 5 \times 7 \times 7 \\ \hline \end{array} $$

and the new marvellous number is $485100$

(thanks to Prajanan Pate for the improvement)

original answer

So the Grand Master scores highly, of course, getting $5 \times 7 \times 11 \times 13 \times 17 \times 19 \times 23 = 37182145$

The remaining disciples, in order round the table, get: $$\begin{array}{|c|c|} \hline \text{Disciple} & \text{Score} & \text{Composition} \\ \hline 1 & 14872858 & 2 \times 7 \times 11 \times 13 \times 17 \times 19 \times 23 \\ \hline 2 & 6374082 & 2 \times 3 \times 11 \times 13 \times 17 \times 19 \times 23 \\ \hline 3 & 2897310 & 2 \times 3 \times 5 \times 13 \times 17 \times 19 \times 23 \\ \hline 4 & 1560090 & 2 \times 3 \times 5 \times 7 \times 17 \times 19 \times 23 \\ \hline 5 & 1009470 & 2 \times 3 \times 5 \times 7 \times 11 \times 19 \times 23 \\ \hline 6 & 690690 & 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 23 \\ \hline 7 & 510510 & 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17 \\ \hline 8 & 4849845 & 3 \times 5 \times 7 \times 11 \times 13 \times 17 \times 19 \\ \hline \end{array} $$

and the "incredible" number is $23\#=223092870$.

... and the field is open for a lower number!