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Elements is best-known for its geometric results, but it also includes many results in number theory, for example the connection between perfect numbers and Mersenne primes, the proof of the infinitude of prime numbers, Euclid's lemma on factorization this leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations, and the Euclidean algorithm for discovering the greatest common divisor of two numbers. Many of the results in Elements originated with earlier mathematicians so one of Euclid's accomplishments was to present them in a single, logically coherent framework, including a system of rigorous mathematical proofs that remains the basis of mathematics twenty-three centuries later...
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