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Generate the first n prime numbers.

Certification: Basic Level Accuracy: 66.67% Submissions: 6 Points: 5

Write a C# program to implement the GeneratePrimes(int n) function, which generates the first n prime numbers. A prime number is a natural number greater than 1 that is not divisible without a remainder by any natural number other than 1 and itself.

Algorithm
    
  
  • Step 1: Start checking numbers from 2 (the first prime number).
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  • Step 2: For each number, check if it's prime by testing divisibility by all smaller primes.
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  • Step 3: If the number is prime, add it to the result list.
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  • Step 4: Continue until you have found n prime numbers.
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Example 1
    
  
  • Input: n = 5
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  • Output: [2, 3, 5, 7, 11]
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  • Explanation: 
      
      
    • The first prime number is 2.
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    • The second prime number is 3.
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    • The third prime number is 5.
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    • The fourth prime number is 7.
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    • The fifth prime number is 11.
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Example 2
    
  
  • Input: n = 10
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  • Output: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
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  • Explanation: 
      
      
    • These are the first 10 prime numbers in ascending order.
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Constraints
    
  
  • 1 ≤ n ≤ 1000
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  • The function should return an array of the first n prime numbers
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  • Time Complexity: O(n * sqrt(n))
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  • Space Complexity: O(n)
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NumberVariables and Data TypesEYSamsung
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Hint
Solution

Solution Hints

    
  
  • Use a combination of trial division and the fact that you only need to check divisibility by primes up to the square root of the number
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  • Keep track of the primes you've already found and use them for testing primality of subsequent numbers
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  • Consider using the Sieve of Eratosthenes algorithm for more efficient prime generation if you need to find many primes
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  • Remember that 2 is the only even prime number
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