section_path: Subclasses of the integers/Prime numbers
section_name: Prime numbers
paragraph_text: Prime numbers
  
  A prime number, often shortened to just prime, is an integer greater than 1 that is not the product of two smaller positive integers. The first few prime numbers are 2, 3, 5, 7, and 11. There is no such simple formula as for odd and even numbers to generate the prime numbers. The primes have been widely studied for more than 2000 years and have led to many questions, only some of which have been answered. The study of these questions belongs to number theory. Goldbach's conjecture is an example of a still unanswered question: "Is every even number the sum of two primes?"
  
  One answered question, as to whether every integer greater than one is a product of primes in only one way, except for a rearrangement of the primes, was confirmed; this proven claim is called the fundamental theorem of arithmetic. A proof appears in Euclid's Elements.