Research and Advances
Computing Applications

Some negative results concerning prime number generators

Posted

Programs attributed to Wirth and Misra for generating the prime numbers up to a specified limit are investigated. It is shown that Wirth's program is incorrect according to three increasingly weak criteria, and a composite number is exhibited that the program accepts as prime. This is the smallest known counterexample, and could not have been found by the usual method of program testing—the program would run for trillions of years on the fastest computer before reaching it! Closely related counterexamples are given to a conjecture of Misra concerning his program. An appendix gives a particularly simple algorithmic proof of the Chinese remainder theorem.

View this article in the ACM Digital Library.

Join the Discussion (0)

Become a Member or Sign In to Post a Comment

The Latest from CACM

Shape the Future of Computing

ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.

Get Involved

Communications of the ACM (CACM) is now a fully Open Access publication.

By opening CACM to the world, we hope to increase engagement among the broader computer science community and encourage non-members to discover the rich resources ACM has to offer.

Learn More