Puzzle 1204 15030

On Dec 19, 2024 Dmitry Kamenetsky wrote:

I found something interesting. If you choose a random prime p less than 15015 then there is a 51.6% chance that (30030-p) is also prime. Essentially primes are symmetrically distributed around 15015. Some questions:

Q1. Is there an explanation for this unusual phenomenon?

Q2. Are there any numbers larger than 15015 that have the same behavior? I wasn't able to find any with a percentage above 50% up to 100,000.

Attached, and below, is a plot I computed. For each n, I compute the percentage of primes p (axis Y) less than n, such that (2n-p) is also prime (axis X).