To solve the problem of determining how many of the years 2027, 2029, 2039, 2053, and 2063 have the sum of their digits equal to a prime number, we need to follow these steps:
1. Break down each year into its individual digits.
2. Calculate the sum of these digits for each year.
3. Check if the resulting sum is a prime number.
4. Count how many of these sums are prime.
Let's start with the given years:
### Year 2027:
- Digits: 2, 0, 2, 7
- Sum of digits: 2 + 0 + 2 + 7 = 11
- Check if 11 is prime: Yes, 11 is a prime number.
### Year 2029:
- Digits: 2, 0, 2, 9
- Sum of digits: 2 + 0 + 2 + 9 = 13
- Check if 13 is prime: Yes, 13 is a prime number.
### Year 2039:
- Digits: 2, 0, 3, 9
- Sum of digits: 2 + 0 + 3 + 9 = 14
- Check if 14 is prime: No, 14 is not a prime number.
### Year 2053:
- Digits: 2, 0, 5, 3
- Sum of digits: 2 + 0 + 5 + 3 = 10
- Check if 10 is prime: No, 10 is not a prime number.
### Year 2063:
- Digits: 2, 0, 6, 3
- Sum of digits: 2 + 0 + 6 + 3 = 11
- Check if 11 is prime: Yes, 11 is a prime number.
### Conclusion:
- Years with the sum of their digits equal to a prime: 2027, 2029, 2063.
- Total number of such years: 3
So, the number of these years that have the sum of their digits equal to a prime is 3.
