Two consecutive odd primes, such as 11 and 13, are called a pair of "twin primes" how many pairs of twin primes are there between 15 and 45?
F-2
G-3
H-4
J-5
K-7
Make a list of odd consecutive pairs. It cannot include 15, 21, 25, 27, 33, 35, 39, or 45.
17 - 19
29 - 31
41 - 43
A total of three
I can't think of any others. Can you?
To find the number of pairs of twin primes between 15 and 45, we need to check each odd number within this range and determine if it is a prime number and if the next odd number is also a prime number.
Starting with the number 15, we can check if it is prime:
- Divide 15 by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14. None of these divisions result in a whole number, so 15 is not a prime number.
Next, we check if 17 is prime:
- Divide 17 by 2. This division does not result in a whole number, so 17 is not divisible by 2.
- Divide 17 by 3. This division does not result in a whole number, so 17 is not divisible by 3.
- Divide 17 by 4. This division does not result in a whole number, so 17 is not divisible by 4.
- Divide 17 by 5. This division does not result in a whole number, so 17 is not divisible by 5.
- Divide 17 by 6. This division does not result in a whole number, so 17 is not divisible by 6.
- Divide 17 by 7. This division does not result in a whole number, so 17 is not divisible by 7.
- Divide 17 by 8. This division does not result in a whole number, so 17 is not divisible by 8.
- Divide 17 by 9. This division does not result in a whole number, so 17 is not divisible by 9.
- Divide 17 by 10. This division does not result in a whole number, so 17 is not divisible by 10.
- Divide 17 by 11. This division does not result in a whole number, so 17 is not divisible by 11.
- Divide 17 by 12. This division does not result in a whole number, so 17 is not divisible by 12.
- Divide 17 by 13. This division does not result in a whole number, so 17 is not divisible by 13.
- Divide 17 by 14. This division does not result in a whole number, so 17 is not divisible by 14.
Based on these calculations, we determine that 17 is a prime number. Now we need to check if the next odd number (19) is also a prime number.
- Divide 19 by 2. This division does not result in a whole number, so 19 is not divisible by 2.
- Divide 19 by 3. This division does not result in a whole number, so 19 is not divisible by 3.
- Divide 19 by 4. This division does not result in a whole number, so 19 is not divisible by 4.
- Divide 19 by 5. This division does not result in a whole number, so 19 is not divisible by 5.
- Divide 19 by 6. This division does not result in a whole number, so 19 is not divisible by 6.
- Divide 19 by 7. This division does not result in a whole number, so 19 is not divisible by 7.
- Divide 19 by 8. This division does not result in a whole number, so 19 is not divisible by 8.
- Divide 19 by 9. This division does not result in a whole number, so 19 is not divisible by 9.
- Divide 19 by 10. This division does not result in a whole number, so 19 is not divisible by 10.
- Divide 19 by 11. This division does not result in a whole number, so 19 is not divisible by 11.
- Divide 19 by 12. This division does not result in a whole number, so 19 is not divisible by 12.
- Divide 19 by 13. This division does not result in a whole number, so 19 is not divisible by 13.
- Divide 19 by 14. This division does not result in a whole number, so 19 is not divisible by 14.
- Divide 19 by 15. This division does not result in a whole number, so 19 is not divisible by 15.
- Divide 19 by 16. This division does not result in a whole number, so 19 is not divisible by 16.
- Divide 19 by 17. This division does not result in a whole number, so 19 is not divisible by 17.
- Divide 19 by 18. This division does not result in a whole number, so 19 is not divisible by 18.
Based on these calculations, we determine that 19 is a prime number. Therefore, we have found one pair of twin primes between 15 and 45, which is (17, 19).
Continuing this process, we check each odd number up to 45 to see if it is prime and if the next odd number is also a prime. Following this process, we find a total of two pairs of twin primes between 15 and 45, which are (17, 19) and (29, 31).
Therefore, the correct answer is F-2.
To find the number of pairs of twin primes between 15 and 45, we need to identify consecutive odd prime numbers within this range.
First, let's list out the prime numbers between 15 and 45: 17, 19, 23, 29, 31, 37, 41, 43.
Next, let's check if any of these consecutive odd primes have a difference of 2.
17 and 19 form a pair of twin primes.
19 and 23 form a pair of twin primes.
29 and 31 form a pair of twin primes.
41 and 43 form a pair of twin primes.
So, there are a total of 4 pairs of twin primes between 15 and 45.
Therefore, the correct answer is H-4.