Here’s a question: if we take the product of the first P prime numbers (we call the product Q), then consider any interval of natural numbers that contain Q, and construct the ratio of non-primes over he size of that interval. We know that the interval (Q-P, P+Q) has a lower bound of nearly 1/2 non-primes, and possibly larger: can we construct a non-Q-like interval with probably larger ratio of non-primes to interval size? The question is about the ratio.