Cray Research Inc. has a buyer for what it predicts will be the world's fastest computer even though the machine doesn't exist yet, not even as a prototype.

The $25 million machine is being ordered two years ahead of scheduled delivery by the Pittsburgh Supercomputing Center, a joint venture of the University of Pittsburgh, Carnegie-Mellon University and Westinghouse Electric Corp.The Cray 3 is expected to be the world's most powerful supercomputer, capable of speeds at least three times as fast as today's quickest machine. Cray hopes to have a prototype ready for testing by the end of the year.

Cray officials said it was the first time the company had committed itself to selling a supercomputer so early in the development stage, and they acknowledged that a great deal of work still must be done.

"There's no reason to believe that we will not be successful," said Edward A. Masi, Cray vice president of marketing. "But you never know until you ship the product."

The Cray 3 is the latest creation of Seymour Cray, who founded Cray Research in 1972. If the machine fulfills its promise, it will represent the fifth time that Cray has set the standard for computer speed and power.

He has said the computer will make as many as 16 billion calculations per second, 10 times as fast as his last machine, the Cray 2, and at least three times as fast as the ETA-10, made by ETA Systems Inc., a Control Data Corp. subsidiary.

It also would be the first commercial computer to be based on semiconductor chips of gallium arsenide rather than silicon, Cray Research said.

Cray is turning to gallium arsenide because electricity passes through the compound more rapidly and dissipates less quickly. The result is a faster chip that uses less power and can be packed more densely into the machine.

The 3-year-old Pittsburgh Supercomputing Center is one of five such centers established around the country with financing from the National Science Foundation.