12 lines
No EOL
1.6 KiB
Text
12 lines
No EOL
1.6 KiB
Text
```json
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{
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"documents": [
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{
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"data": "Algorithm: Sieve of Eratosthenes to Calculate First 1000 Prime Numbers\n\n1. Initialize Variables:\n - Let n be an upper bound estimate for the 1000th prime number. A safe estimate is n = 7920, since the 1000th prime is 7919.\n - Create a boolean array `isPrime` of size n+1, initialized to true. This array will help track prime numbers.\n - Set `isPrime[0]` and `isPrime[1]` to false, as 0 and 1 are not prime numbers.\n\n2. Implement the Sieve of Eratosthenes:\n - For each integer p from 2 to √n:\n a. If `isPrime[p]` is true, it means p is a prime number.\n b. Mark all multiples of p (starting from p^2) as false in the `isPrime` array, as they are not prime.\n\n3. Collect Prime Numbers:\n - Initialize an empty list `primes` to store prime numbers.\n - Iterate over the `isPrime` array:\n a. For each index i where `isPrime[i]` is true, add i to the `primes` list.\n b. Stop collecting once the list contains 1000 prime numbers.\n\n4. Return the List of Primes:\n - The `primes` list now contains the first 1000 prime numbers.\n\nValidation:\n- Ensure that the length of the `primes` list is exactly 1000.\n- Verify that the last element in the `primes` list is 7919, the 1000th prime number.\n\nThis algorithm efficiently calculates the first 1000 prime numbers using the Sieve of Eratosthenes, which has a time complexity of O(n log log n).",
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"mimeType": "text/plain",
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"comment": "This document describes an efficient algorithm to calculate the first 1000 prime numbers using the Sieve of Eratosthenes."
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}
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],
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"continue": false
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}
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``` |