Suppose when searching for a large prime, our first step is to sieve by eliminating the first n primes. How large should n be to speed up our search by a factor of $10?$ This requires careful thought and inventiveness before doing a computation. How to approach this: Eliminating all odd numbers speeds up our program by a factor of $2,$ since we've eliminated half of the choices that are composite. If we also immediately disqualify multiples of $3,$ then we speed up our program by a factor of $3,$ since we have eliminated $2/3$ of all composites. Check that that argument is correct. Now see what happens when you eliminate all of $2,3$ and $5.$ Again for $2,3,5,7.$ Now try to figure out the mathematical result and use it to solve for n$.$