The *primorial* of a number is the product of all the prime numbers less than or equal to that number. For example, the primorial of \(6\) is \(2 \times 3 \times 5 = 30\).

How many different whole numbers have a primorial of \(210\)?

From the question, we know that the primorial of \(6\) is less than \(210\), so no number less than \(6\) will have a primorial of \(210\).

The primorial of \(7\) is \(2 \times 3 \times 5 \times 7 = 210\). Since \(8\), \(9\) and \(10\) are not prime numbers, they too have a primorial of \(210\).

Any number greater than or equal to \(11\) will have a primorial of at least \(2 \times 3 \times 5 \times 7 \times 11 = 2310\).

So there are exactly \(4\) integers with a primorial of \(210\).