Generate Prime Numbers with Python

Introduction

In mathematics, prime numbers are natural numbers greater than 1 that are not divisible by any other number except 1 and itself. Generating a list of prime numbers is a common problem in computer science and has various applications in cryptography, number theory, and other fields.

Skills Graph

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Generate Primes

Problem

Write a Python function that generates a list of prime numbers. The function should take an integer as input and return a list of Boolean values, where each value corresponds to whether the index is a prime number or not. For example, if the input is 20, the output should be [False, False, True, True, False, True, False, True, False, False, False, True, False, True, False, False, False, True, False, True], where the value at index 2 is True because 2 is a prime number, and the value at index 4 is False because 4 is not a prime number.

Requirements

The function should not consider 1 as a prime number.
The function should handle invalid inputs by raising an exception.
The function should generate the list of prime numbers in memory.

Example Usage

None -> Exception
Not an int -> Exception
20 -> [False, False, True, True, False, True, False, True, False, False, False, True, False, True, False, False, False, True, False, True]

Summary

Generating a list of prime numbers is a fundamental problem in computer science. By following the requirements and example usage, you can write a Python function that generates a list of prime numbers and use it in various applications.

Generate Prime Numbers