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How many prime number are there between 100 to 500 . Can you?
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How many prime number are there between 100 to 500 . Can you?
Counting Prime Numbers between 100 and 500


Prime numbers are those numbers that are only divisible by 1 and itself. In order to count the number of prime numbers between 100 and 500, we need to first understand the concept of prime numbers.


What is a Prime Number?


A prime number is a positive integer that is divisible by only 1 and itself. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 are the first 25 prime numbers.


Counting Prime Numbers between 100 and 500


In order to count the number of prime numbers between 100 and 500, we need to check each number between 100 and 500 to see if it is a prime number. There are different methods to check if a number is prime or not, but the most common method is to use the Sieve of Eratosthenes.


The Sieve of Eratosthenes


The Sieve of Eratosthenes is a simple and efficient algorithm for finding all prime numbers up to a specified integer. The algorithm works by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the multiples of 2.


Counting Prime Numbers between 100 and 500 using Sieve of Eratosthenes


Using the Sieve of Eratosthenes, we can create a list of all the prime numbers between 2 and 500. Then, we can count the number of prime numbers between 100 and 500 by simply checking which numbers in the list are between 100 and 500. Here are the steps:



  1. Create a list of all the numbers between 2 and 500.

  2. Start with the first prime number, 2.

  3. Mark all the multiples of 2 as composite.

  4. Move to the next unmarked number, 3, which is prime.

  5. Mark all the multiples of 3 as composite.

  6. Repeat steps 4 and 5 until you have marked all the multiples of all the prime numbers less than or equal to the square root of 500.

  7. The remaining unmarked numbers are all prime.

  8. Count the number of prime numbers between 100 and 500.



Answer


Using the Sieve of Eratosthenes, we can find that there are 65 prime numbers between 100 and 500.


Therefore, the answer to the question is that there are 65 prime numbers between 100 and 500.
Community Answer
How many prime number are there between 100 to 500 . Can you?
I think 70
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