The KPROC (KiloPROCessor) architecture is the first implementation of a parallel computer with 1024 floating-point processors on a single chip. It strictly follows the concept of an instruction systolic array. The modular organisation allows for either building large arrays of many KPROC chips or speeding up small machines with a single KPROC as a coprocessor. This paper presents concept of this parallel computer model as well as the architectural details of the processor design. It is shown that this computer model allows for efficient implementation of parallel prefix computations. A large variety of applications from different areas is presented to demonstrate how parallel prefix computations can be used as key operations for deriving efficient implementations on the KPROC.