To solve the problem of finding how many prime days there are in a non-leap year, let's break down the steps:
1. Understand Prime Numbers:
- A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Examples of prime numbers less than 32 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
2. Identify Prime Numbers for Months:
- We are dealing with the months of the year, which range from 1 to 12.
- Among these, the prime months are: 2 (February), 3 (March), 5 (May), 7 (July), and 11 (November).
3. Prime Days in Prime Months:
- Each of these prime months has a different number of days, and we need to count the prime days within these months.
- Since we are only interested in prime days, we must list out the prime days that can occur in any month. Prime numbers up to 31 (since some months have 31 days) are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
4. Calculate the Number of Prime Days in Each Prime Month:
- For February (28 days):
- Prime days: 2, 3, 5, 7, 11, 13, 17, 19, 23
- Count: 9 prime days
- For March (31 days):
- Prime days: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
- Count: 11 prime days
- For May (31 days):
- Prime days: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
- Count: 11 prime days
- For July (31 days):
- Prime days: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
- Count: 11 prime days
- For November (30 days):
- Prime days: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
- Count: 10 prime days
5. Sum the Prime Days Across All Prime Months:
- February: 9 prime days
- March: 11 prime days
- May: 11 prime days
- July: 11 prime days
- November: 10 prime days
Total = 9 + 11 + 11 + 11 + 10 = 52 prime days
Thus, in a non-leap year, there are 52 prime days.
