The concept of primes and the algorithm for counting the greatest common divisor in Ancient China

TL;DR

This paper demonstrates that the ancient Chinese had concepts of primes and an algorithm for GCD calculation predating Greek mathematics, challenging common historical assumptions.

Contribution

It provides historical evidence that the concept of primes and GCD algorithms existed in Ancient China centuries before their recognition in Western mathematics.

Findings

The concept of primes in China dates back to around 500 B.C.

The Chinese GCD algorithm is essentially the Euclidean algorithm.

Ancient Chinese GCD algorithm predates Stein's binary GCD algorithm.

Abstract

When people mention the number theoretical achievements in Ancient China, the famous Chinese Remainder Theorem always springs to mind. But, two more of them--the concept of primes and the algorithm for counting the greatest common divisor, are rarely spoken. Some scholars even think that Ancient China has not the concept of primes. The aim of this paper is to show that the concept of primes in Ancient China can be traced back to the time of Confuciusor (about 500 B.C.) or more ago. This implies that the concept of primes in Ancient China is much earlier than the concept of primes in Euclid's \emph{Elements}(about 300 B.C.) of Ancient Greece. We also shows that the algorithm for counting the greatest common divisor in Ancient China is essentially the Euclidean algorithm or the binary gcd algorithm. Donald E. Knuth said that "the binary gcd algorithm was discovered by J. Stein in 1961". Nevertheless, Knuth was wrong. The ancient Chinese algorithm is clearly much earlier than J. Stein's algorithm.