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"The way you write science fiction is: you sit down at your writing machine and you open your mind to the first thought that comes through."
- Frederik Pohl

Supercalculator  
  Connecting all the computing machines of the universe!  

Well, nobody ever accused science fiction writers of thinking small...

He straightened and nodded to Dwar Reyn, then moved to a position beside the switch that would complete the contact when he threw it. The switch that would connect, all at once, all of the monster computing machines of all the populated planets in the universe—ninety-six billion planets—into the supercircuit that would connect them all into one supercalculator, one cybernetics machine that would combine all the knowledge of all the galaxies.Dwar Reyn spoke briefly to the watching and listening trillions. Then after a moment’s silence he said, “Now, Dwar Ev.”Dwar Ev threw the switch. There was a mighty hum, the surge of power from ninety-six billion planets. Lights flashed and quieted along the miles-long panel.
Technovelgy from Answer, by Frederic Brown.
Published by Dutton in 1954
Additional resources -

Thanks to @SFFaudio, here's a brief clip of Michael Crichton describing the Turing test, and Chuck Heston giving away the ending of this very short story.

Compare to metal calculator planet from Limiting Factor (1949) by Clifford Simak and gigagnostotron from The Cyberiad: Fables for the Cybernetic Age (1965) by Stanislaw Lem.

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Additional resources:
  More Ideas and Technology from Answer
  More Ideas and Technology by Frederic Brown
  Tech news articles related to Answer
  Tech news articles related to works by Frederic Brown

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