Chapter 10 Primes
Produce a list of all prime numbers up to a given natural number.
Compute the prime factorization of a number.
Show whether a number is prime.
Show that there are infinitely many prime numbers.
Show that twin primes exist.
Reproduce the twin prime conjecture.
Prime numbers are a cornerstone of mathematics. Their lack of divisors makes them valuable numbers to work with. In this section we introduce the fundamental concepts of primality and prime factorization. We show that there are infinitely many prime numbers and present an important conjecture about primes.