To find the sum of all prime numbers between 60 and 80, we can follow these steps:
### Step 1: Identify the prime numbers between 60 and 80
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. We need to check each number between 60 and 80 to see if it is prime.
- **61**: Prime (divisible only by 1 and 61)
- **62**: Not prime (divisible by 1, 2, 31, 62)
- **63**: Not prime (divisible by 1, 3, 7, 9, 21, 63)
- **64**: Not prime (divisible by 1, 2, 4, 8, 16, 32, 64)
- **65**: Not prime (divisible by 1, 5, 13, 65)
- **66**: Not prime (divisible by 1, 2, 3, 6, 11, 22, 33, 66)
- **67**: Prime (divisible only by 1 and 67)
- **68**: Not prime (divisible by 1, 2, 4, 17, 34, 68)
- **69**: Not prime (divisible by 1, 3, 23, 69)
- **70**: Not prime (divisible by 1, 2, 5, 7, 10, 14, 35, 70)
- **71**: Prime (divisible only by 1 and 71)
- **72**: Not prime (divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72)
- **73**: Prime (divisible only by 1 and 73)
- **74**: Not prime (divisible by 1, 2, 37, 74)
- **75**: Not prime (divisible by 1, 3, 5, 15, 25, 75)
- **76**: Not prime (divisible by 1, 2, 4, 19, 38, 76)
- **77**: Not prime (divisible by 1, 7, 11, 77)
- **78**: Not prime (divisible by 1, 2, 3, 6, 13, 26, 39, 78)
- **79**: Prime (divisible only by 1 and 79)
The prime numbers between 60 and 80 are: **61, 67, 71, 73, and 79**.
### Step 2: Calculate the sum of the identified prime numbers
Now we will add these prime numbers together:
\[
61 + 67 + 71 + 73 + 79
\]
Calculating step by step:
1. \(61 + 67 = 128\)
2. \(128 + 71 = 199\)
3. \(199 + 73 = 272\)
4. \(272 + 79 = 351\)
### Final Answer
The sum of all prime numbers between 60 and 80 is **351**.
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