Verhoeff algorithm

The Verhoeff algorithm is a checksum for error detection first published by Dutch mathematician Jacobus Verhoeff in 1969. It was the first decimal check digit algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits, which was at the time thought impossible with such a code.

The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to any base.