Prime Time Again Problem Statement

You are given two integers DAY_HOURS and PARTS. The integer 'DAY_HOURS' represents the number of hours in a day, and the day can be divided into 'PARTS' equal parts. Your task is to determine the total instances of equivalent prime groups. A prime group refers to a pair of hours that are both prime and measure the same equivalent time from the start of the day, but each hour is in a different part of the day.

Example:

Input:

DAY_HOURS = 20, PARTS = 2

Output:

2

Explanation:

The day can be represented in parts as follows:

1  2  3  4  5  6  7  8  9 10  - Part 1
11 12 13 14 15 16 17 18 19 20 - Part 2

The prime groups are (3, 13) and (7, 17), as both elements in each pair are prime numbers.

Constraints:

• 1 ≤ T ≤ 100
• 10 ≤ DAY_HOURS ≤ 5 * 103
• 2 ≤ PARTS ≤ 103
• The day should be evenly divided by parts (i.e., DAY_HOURS % PARTS == 0).
• Time Limit: 1 second

Note:

1. The day starts at hour 1 and ends at hour 'DAY_HOURS'.
2. Each hour of the prime group must be from different parts of the day.
3. If there are no equivalent prime groups, return zero.
4. The number of hours per part must be a natural number.