# Sample Projects

## Extension of central pharmaceutical number for medicines

To ensure unambiguous identification of medicines in Germany, each product is assigned a unique PZN (Pharmazentralnummer = central pharmaceutical number) by IFA GmbH. Prior to 2013, the PZN was seven digits in length, of which the seventh served as a check digit. Its presence meant that false entries were avoided. With the seven-digit PZN, only 909,090 numbers were possible. As the seven-digit numbers were almost used up, the PZN had to be extended by more digits. The extension process required that the previous seven-digit PZNs should remain valid and that the entry of invalid codes would continue to be reliably prevented in the future.

The calculation of the check digit is carried out in the field of integers modulo 11. This is a finite field which plays an important role in cryptography and coding theory. It turned out that it was possible to extend the PZN to eight digits, thereby increasing the number of PZNs approximately tenfold. This extension was carried out in early 2013. The check digit is now in eighth position. The check digit system continues to prevent single errors, exchange errors and almost all cases of twin errors.

The calculations showed that the PZN could theoretically be extended to as many as eleven digits, which would then generate 25,937,424,600 PZNs, i.e. just under 26 billions. At this point, however, a limit would be reached, and the only possibility for developing a new and even more comprehensive system would be to recalculate and reissue all previous PZNs.