Find the sum of all primes q<1000 such that for some prime p<q , both q divides p^3-1 and p divides q^3-1

To find the primes q < 1000 that satisfy the given conditions, we need to check each prime number p and then verify if q exists for each valid p.

First, let's generate a list of prime numbers p < 1000:
1. Initialize an empty list of prime numbers.
2. Start with p = 2 and iterate until p < 1000.
3. For each value of p, check if it is prime:
a. Iterate from i = 2 to sqrt(p) and check if p is divisible by any i.
b. If p is divisible by any i, it is not prime, so break out of the loop.
c. If p is not divisible by any i, append it to the list of primes.

Now, we have a list of prime numbers p < 1000. For each p, we need to find the prime number q that satisfies the given conditions.

To check if q exists, we can iterate through each prime number p and check if there is a prime number q that satisfies both conditions (q divides p^3 - 1 and p divides q^3 - 1).

For each p, we can iterate through all prime numbers q less than p until we find one that satisfies the conditions.

Let's go ahead and implement this solution.