Editing Number (section)

===Prime numbers {{anchor|History of prime numbers}}===
[[Prime number]]s have been studied throughout recorded history.{{Citation needed|reason=Wikipedia's prime number article says the Greeks were the first to explicitly study prime numbers and mentions only the Rhind Papyrus as implicitly recognizing a distinction between prime and composite numbers.|date=September 2020}} They are positive integers that are divisible only by 1 and themselves. Euclid devoted one book of the ''Elements'' to the theory of primes; in it he proved the infinitude of the primes and the [[fundamental theorem of arithmetic]], and presented the [[Euclidean algorithm]] for finding the [[greatest common divisor]] of two numbers.

In 240 BC, [[Eratosthenes]] used the [[Sieve of Eratosthenes]] to quickly isolate prime numbers. But most further development of the theory of primes in Europe dates to the [[Renaissance]] and later eras.{{Citation needed|reason=Need citation for activity (or lack thereof) during era between Eratosthenes and Legendre.|date=September 2020}}

In 1796, [[Adrien-Marie Legendre]] conjectured the [[prime number theorem]], describing the asymptotic distribution of primes. Other results concerning the distribution of the primes include Euler's proof that the sum of the reciprocals of the primes diverges, and the [[Goldbach conjecture]], which claims that any sufficiently large even number is the sum of two primes. Yet another conjecture related to the distribution of prime numbers is the [[Riemann hypothesis]], formulated by [[Bernhard Riemann]] in 1859. The [[prime number theorem]] was finally proved by [[Jacques Hadamard]] and [[Charles de la Vallée-Poussin]] in 1896. Goldbach and Riemann's conjectures remain unproven and unrefuted.