6. A semiprime is a number that is a product of two prime numbers. How many semiprime numbers less than 2018 can be expressed as $x^{3}-1$ for some natural number $x$ ?
Answer: 4
Solution: $x^{3}-1=(x-1)\left(x^{2}+x+1\right)$, so this implies that both $x-1$ and $x^{2}+x+1$ have to be prime. Furthermore, this also means we only have numbers up to 12 to work on, as $13^{3}>2018$. Hence, we only have to check $x=3,4,6,8,12$ and determine if $x^{2}+x+1$ is prime.

The values we get are $13,21,43,73,157$, and of the 5 , only 4 are prime.