- #1
TimNguyen
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How would I write a program that finds all the prime numbers that are less than or equal to a "user-supplied" integer N, implementing the fact that I should only be dividing N by all prime numbers less than sqrt(N)?
A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has exactly two factors.
One method is to use the "Sieve of Eratosthenes" algorithm, which involves systematically eliminating all the multiples of each prime number starting from 2 up to the given number, N. The remaining numbers after this process are the prime numbers up to N.
As of June 2021, the largest known prime number is 2^82,589,933 – 1, which has over 24 million digits. It was discovered in December 2018.
While there are some patterns and rules that can help identify prime numbers, such as the fact that all prime numbers greater than 3 are of the form 6n ± 1, there is no known formula or algorithm that can generate all prime numbers.
Prime numbers play a crucial role in cryptography, as they are used in creating secure encryption methods. They also have applications in various fields such as number theory, computer science, and physics. Additionally, prime numbers are fundamental building blocks in the study of mathematics and help us better understand the properties of numbers.