26 lines
No EOL
1.3 KiB
Text
26 lines
No EOL
1.3 KiB
Text
Algorithm: Sieve of Eratosthenes to Calculate First 1000 Prime Numbers
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1. Initialize Variables:
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- Let n be an upper bound estimate for the 1000th prime number. A safe estimate is n = 7920, since the 1000th prime is 7919.
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- Create a boolean array `isPrime` of size n+1, initialized to true. This array will help track prime numbers.
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- Set `isPrime[0]` and `isPrime[1]` to false, as 0 and 1 are not prime numbers.
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2. Implement the Sieve of Eratosthenes:
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- For each integer p from 2 to √n:
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a. If `isPrime[p]` is true, it means p is a prime number.
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b. Mark all multiples of p (starting from p^2) as false in the `isPrime` array, as they are not prime.
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3. Collect Prime Numbers:
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- Initialize an empty list `primes` to store prime numbers.
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- Iterate over the `isPrime` array:
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a. For each index i where `isPrime[i]` is true, add i to the `primes` list.
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b. Stop collecting once the list contains 1000 prime numbers.
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4. Return the List of Primes:
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- The `primes` list now contains the first 1000 prime numbers.
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Validation:
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- Ensure that the length of the `primes` list is exactly 1000.
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- Verify that the last element in the `primes` list is 7919, the 1000th prime number.
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This algorithm efficiently calculates the first 1000 prime numbers using the Sieve of Eratosthenes, which has a time complexity of O(n log log n). |