Some negative results concerning prime number generators
By Paul Pritchard
Communications of the ACM,
Vol. 27 No. 1, Pages 53-57
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.
The full text of this article is premium content
No entries found
Log in to Read the Full Article
Purchase the Article
Create a Web Account
If you are an ACM member, Communications subscriber, Digital Library subscriber, or use your institution's subscription, please set up a web account to access premium content and site
features. If you are a SIG member or member of the general public, you may set up a web account to comment on free articles and sign up for email alerts.