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When people mention the number theoretical achievements in Ancient China, thefamous Chinese Remainder Theorem always springs to mind. But, two more ofthem--the concept of primes and the algorithm for counting the greatest commondivisor, are rarely spoken. Some scholars even think that Ancient China has notthe concept of primes. The aim of this paper is to show that the concept ofprimes in Ancient China can be traced back to the time of Confuciusor (about500 B.C.) or more ago. This implies that the concept of primes in Ancient Chinais much earlier than the concept of primes in Euclid's \emph{Elements}(about300 B.C.) of Ancient Greece. We also shows that the algorithm for counting thegreatest common divisor in Ancient China is essentially the Euclidean algorithmor the binary gcd algorithm. Donald E. Knuth said that "the binary gcdalgorithm was discovered by J. Stein in 1961". Nevertheless, Knuth was wrong.The ancient Chinese algorithm is clearly much earlier than J. Stein'salgorithm.

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