Final answer:
To show that there are no prime numbers between 7,608 and 7,620, we can check each number in the given range to see if it is divisible by any prime numbers less than its square root. If it is divisible by any of these prime numbers, then it is not a prime number.
Step-by-step explanation:
To show that there are no prime numbers between 7,608 and 7,620, we can check each number in the given range to see if it is divisible by any prime numbers less than its square root. If it is divisible by any of these prime numbers, then it is not a prime number.
Let's check each number in the range:
- 7,608: Not divisible by 2, 3, 5, or 7. Possible prime.
- 7,609: Divisible by 17. Not a prime number.
- 7,610: Divisible by 2, 5, or 7. Not a prime number.
- 7,611: Divisible by 59. Not a prime number.
- 7,612: Divisible by 2, 3, or 7. Not a prime number.
- 7,613: Possible prime.
- 7,614: Divisible by 2, 3, 5, or 7. Not a prime number.
- 7,615: Divisible by 5 or 7. Not a prime number.
- 7,616: Divisible by 2, 7, or 17. Not a prime number.
- 7,617: Divisible by 3. Not a prime number.
- 7,618: Divisible by 2, 7, or 59. Not a prime number.
- 7,619: Possible prime.
- 7,620: Divisible by 2, 3, 5, or 7. Not a prime number.
From the above checks, we can see that the numbers 7,609, 7,610, 7,611, 7,612, 7,615, 7,616, 7,617, 7,618, and 7,620 are not prime.
Therefore, there are no prime numbers between 7,608 and 7,620.