Identifying Prime Numbers Between 306 and 313
The problem asks for the count of prime numbers within the range of 306 to 313, inclusive.
Step 1: List the numbers in the range.
The numbers to consider are: 306, 307, 308, 309, 310, 311, 312, 313.
Step 2: Define a prime number.
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
Step 3: Check each number for primality.
- 306: Divisible by 2 (it's even). Not prime.
- 307: Not divisible by 2, 3 (sum of digits is 10), 5. Test divisibility by primes up to $\sqrt{307} \approx 17.5$ (i.e., 7, 11, 13, 17). 307 is not divisible by any of these. Prime.
- 308: Divisible by 2 (it's even). Not prime.
- 309: Divisible by 3 (sum of digits is 12). Not prime.
- 310: Divisible by 2 and 5 (ends in 0). Not prime.
- 311: Not divisible by 2, 3 (sum of digits is 5), 5. Test divisibility by primes up to $\sqrt{311} \approx 17.6$ (i.e., 7, 11, 13, 17). 311 is not divisible by any of these. Prime.
- 312: Divisible by 2 (it's even). Not prime.
- 313: Not divisible by 2, 3 (sum of digits is 7), 5. Test divisibility by primes up to $\sqrt{313} \approx 17.7$ (i.e., 7, 11, 13, 17). 313 is not divisible by any of these. Prime.
Step 4: Count the prime numbers found.
The prime numbers identified in the range are 307, 311, and 313.
Conclusion: There are 3 prime numbers between 306 and 313, inclusive.
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Important Questions from Prime Numbers
The number whose only factors are 1 and the number itself is called a/an ________ number.
Consider the following numbers :
1. 437
2. 797
3. 1073
How many of the above numbers are prime ?
What are the total prime numbers from 1 to 100?
How many prime numbers are there between 20 and 50?
How many prime numbers are there between 100 and 120?
