Sum of all the prime numbers between 70 and 100 is :
Understanding Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We need to find all such numbers that fall strictly between 70 and 100.
Identifying Prime Numbers Between 70 and 100
Let's list the numbers between 70 and 100 and check if they are prime. We can exclude even numbers (except 2, which is not in this range) and multiples of 5 easily. For other numbers, we check for divisibility by small prime numbers like 3, 7, etc.
Numbers between 70 and 100 are 71, 72, 73, ..., 99.
- 71: Not divisible by 2, 3, 5, 7. It is a prime number.
- 72: Divisible by 2. Not prime.
- 73: Not divisible by 2, 3, 5, 7. It is a prime number.
- 74: Divisible by 2. Not prime.
- 75: Divisible by 5. Not prime.
- 76: Divisible by 2. Not prime.
- 77: Divisible by 7 ($77 = 7 \times 11$). Not prime.
- 78: Divisible by 2. Not prime.
- 79: Not divisible by 2, 3, 5, 7. It is a prime number.
- 80: Divisible by 2. Not prime.
- 81: Divisible by 3 ($8+1=9$, which is divisible by 3). Not prime.
- 82: Divisible by 2. Not prime.
- 83: Not divisible by 2, 3, 5, 7. It is a prime number.
- 84: Divisible by 2. Not prime.
- 85: Divisible by 5. Not prime.
- 86: Divisible by 2. Not prime.
- 87: Divisible by 3 ($8+7=15$, which is divisible by 3). Not prime.
- 88: Divisible by 2. Not prime.
- 89: Not divisible by 2, 3, 5, 7. It is a prime number.
- 90: Divisible by 2. Not prime.
- 91: Divisible by 7 ($91 = 7 \times 13$). Not prime.
- 92: Divisible by 2. Not prime.
- 93: Divisible by 3 ($9+3=12$, which is divisible by 3). Not prime.
- 94: Divisible by 2. Not prime.
- 95: Divisible by 5. Not prime.
- 96: Divisible by 2. Not prime.
- 97: Not divisible by 2, 3, 5, 7. It is a prime number.
- 98: Divisible by 2. Not prime.
- 99: Divisible by 3 ($9+9=18$, which is divisible by 3). Not prime.
The prime numbers between 70 and 100 are 71, 73, 79, 83, 89, and 97.
| Number | Is Prime? |
|---|---|
| 71 | Yes |
| 73 | Yes |
| 79 | Yes |
| 83 | Yes |
| 89 | Yes |
| 97 | Yes |
Calculating the Sum of Prime Numbers
Now we need to find the sum of these identified prime numbers:
\( \text{Sum} = 71 + 73 + 79 + 83 + 89 + 97 \)
Let's add them step-by-step:
\( 71 + 73 = 144 \)
\( 144 + 79 = 223 \)
\( 223 + 83 = 306 \)
\( 306 + 89 = 395 \)
\( 395 + 97 = 492 \)
The sum of all the prime numbers between 70 and 100 is 492.
Therefore, the correct sum is 492.
Important Questions from Prime Numbers
Which of the following is NOT a pair of co-prime numbers?
a and b are two positive integers such that the least prime factor of a is 2 and the least prime factor of b is 5. Then the least prime factor of a + b is
Which of the following is a pair of coprime numbers ?
If product of two prime numbers A and B (A < B) is 221, then what is the value of (4A – 3B)?
Which one of the following numbers is a prime number?
