The sum of all prime numbers between 58 and 68 is

Options

A. 179
B. 178
C. 187
D. 183

Answer

To find the sum of all prime numbers between 58 and 68, we can follow these steps:

### Step 1: Identify the prime numbers between 58 and 68
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. We will check each number from 59 to 67 (since 68 is not included) to see if it is prime.

- **59**: Check divisibility by 2, 3, 5, and 7 (the primes less than √59). It is not divisible by any of these, so **59 is prime**.
- **60**: Divisible by 2 (60 = 2 × 30), so **60 is not prime**.
- **61**: Check divisibility by 2, 3, 5, and 7. It is not divisible by any of these, so **61 is prime**.
- **62**: Divisible by 2 (62 = 2 × 31), so **62 is not prime**.
- **63**: Divisible by 3 (63 = 3 × 21), so **63 is not prime**.
- **64**: Divisible by 2 (64 = 2 × 32), so **64 is not prime**.
- **65**: Divisible by 5 (65 = 5 × 13), so **65 is not prime**.
- **66**: Divisible by 2 (66 = 2 × 33), so **66 is not prime**.
- **67**: Check divisibility by 2, 3, 5, and 7. It is not divisible by any of these, so **67 is prime**.

The prime numbers between 58 and 68 are **59, 61, and 67**.

### Step 2: Calculate the sum of the identified prime numbers
Now we will add the prime numbers we found:

\[ 59 + 61 + 67 \]

### Step 3: Perform the addition
1. First, add 59 and 61:
\[ 59 + 61 = 120 \]
2. Now, add 67 to the result:
\[ 120 + 67 = 187 \]

### Final Answer
The sum of all prime numbers between 58 and 68 is **187**.

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