One basic instrument in number theory and cryptography is to work with large numbers.

Piologie. An exact arithmetical library in C++

published at Technical Report WSI 96-35 at the Department of Computing Science of the University of Tuebingen, 1996

The mathematical library to calculate with numbers of arbitrary precision runs on every platform. The latest stable version is 1.3.3. It is also available on mobile devices

Many computational records were done based on it:

• zeta(3) record, Number Theory List (NMBRTHRY@LISTSERV.NODAK.EDU), December 1998.
• Exp(1): 869,894,101 decimal digits, Number Theory List (NMBRTHRY@LISTSERV.NODAK.EDU), October 1999.
• http://en.wikipedia.org/wiki/Apéry%27s_constant
• http://mathworld.wolfram.com/AperysConstant.html
• http://de.wikipedia.org/wiki/Eulersche_Zahl
• …

But more relevant are the factorization algorithms.