The Legendre sieve is a mathematical algorithm used in number theory for finding prime numbers within a certain range. It is based on the idea of sieving out composite numbers from a list of integers by marking the multiples of each prime number. Here's an overview of how the Legendre sieve works: 1. **Initialization**: You start with a range of integers, such as all integers from \( 2 \) to \( n \), where \( n \) is your upper limit.
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