Review question

# What is the primorial of a number? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8811

## Solution

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 $210$.